.. _term_table_basic:

.. raw:: latex

   \newpage
Table of basic terms
""""""""""""""""""""

.. tabularcolumns:: |p{0.2\linewidth}|p{0.2\linewidth}|p{0.6\linewidth}|
.. list-table:: Basic terms
   :widths: 20 20 60
   :header-rows: 1
   :class: longtable

   * - name/class
     - arguments
     - definition
   * - dw_advect_div_free

       :class:`AdvectDivFreeTerm <sfepy.terms.terms_diffusion.AdvectDivFreeTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Omega} \nabla \cdot (\ul{y} p) q = \int_{\Omega}
           (\underbrace{(\nabla \cdot \ul{y})}_{\equiv 0} + \ul{y} \cdot
           \nabla) p) q
   * - dw_bc_newton

       :class:`BCNewtonTerm <sfepy.terms.terms_dot.BCNewtonTerm>`
     - ``<material_1>``, ``<material_2>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Gamma} \alpha q (p - p_{\rm outer})
   * - ev_biot_stress

       :class:`BiotStressTerm <sfepy.terms.terms_biot.BiotStressTerm>`
     - ``<material>``, ``<parameter>``
     - .. math::
            - \int_{\Omega} \alpha_{ij} \bar{p}

       .. math::
            \mbox{vector for } K \from \Ical_h: - \int_{T_K}
           \alpha_{ij} \bar{p} / \int_{T_K} 1

       .. math::
            - \alpha_{ij} \bar{p}|_{qp}
   * - dw_biot

       :class:`BiotTerm <sfepy.terms.terms_biot.BiotTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``

       ``<material>``, ``<state>``, ``<virtual>``

       ``<material>``, ``<parameter_v>``, ``<parameter_s>``
     - .. math::
            \int_{\Omega} p\ \alpha_{ij} e_{ij}(\ul{v}) \mbox{ , }
           \int_{\Omega} q\ \alpha_{ij} e_{ij}(\ul{u})
   * - ev_cauchy_strain_s

       :class:`CauchyStrainSTerm <sfepy.terms.terms_elastic.CauchyStrainSTerm>`
     - ``<parameter>``
     - .. math::
            \int_{\Gamma} \ull{e}(\ul{w})

       .. math::
            \mbox{vector for } K \from \Ical_h: \int_{T_K}
           \ull{e}(\ul{w}) / \int_{T_K} 1

       .. math::
            \ull{e}(\ul{w})|_{qp}
   * - ev_cauchy_strain

       :class:`CauchyStrainTerm <sfepy.terms.terms_elastic.CauchyStrainTerm>`
     - ``<parameter>``
     - .. math::
            \int_{\Omega} \ull{e}(\ul{w})

       .. math::
            \mbox{vector for } K \from \Ical_h: \int_{T_K}
           \ull{e}(\ul{w}) / \int_{T_K} 1

       .. math::
            \ull{e}(\ul{w})|_{qp}
   * - ev_cauchy_stress

       :class:`CauchyStressTerm <sfepy.terms.terms_elastic.CauchyStressTerm>`
     - ``<material>``, ``<parameter>``
     - .. math::
            \int_{\Omega} D_{ijkl} e_{kl}(\ul{w})

       .. math::
            \mbox{vector for } K \from \Ical_h: \int_{T_K} D_{ijkl}
           e_{kl}(\ul{w}) / \int_{T_K} 1

       .. math::
            D_{ijkl} e_{kl}(\ul{w})|_{qp}
   * - dw_contact_plane

       :class:`ContactPlaneTerm <sfepy.terms.terms_surface.ContactPlaneTerm>`
     - ``<material_f>``, ``<material_n>``, ``<material_a>``, ``<material_b>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Gamma} \ul{v} \cdot f(d(\ul{u})) \ul{n}
   * - dw_contact_sphere

       :class:`ContactSphereTerm <sfepy.terms.terms_surface.ContactSphereTerm>`
     - ``<material_f>``, ``<material_c>``, ``<material_r>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Gamma} \ul{v} \cdot f(d(\ul{u})) \ul{n}(\ul{u})
   * - dw_contact

       :class:`ContactTerm <sfepy.terms.terms_contact.ContactTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Gamma_{c}} \varepsilon_N \langle g_N(\ul{u})
           \rangle \ul{n} \ul{v}
   * - dw_convect_v_grad_s

       :class:`ConvectVGradSTerm <sfepy.terms.terms_diffusion.ConvectVGradSTerm>`
     - ``<virtual>``, ``<state_v>``, ``<state_s>``
     - .. math::
            \int_{\Omega} q (\ul{u} \cdot \nabla p)
   * - dw_convect

       :class:`ConvectTerm <sfepy.terms.terms_navier_stokes.ConvectTerm>`
     - ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Omega} ((\ul{u} \cdot \nabla) \ul{u}) \cdot \ul{v}
   * - ev_def_grad

       :class:`DeformationGradientTerm <sfepy.terms.terms_hyperelastic_base.DeformationGradientTerm>`
     - ``<parameter>``
     - .. math::
            \ull{F} = \pdiff{\ul{x}}{\ul{X}}|_{qp} = \ull{I} +
           \pdiff{\ul{u}}{\ul{X}}|_{qp} \;, \\ \ul{x} = \ul{X} + \ul{u} \;, J
           = \det{(\ull{F})}
   * - dw_dg_advect_laxfrie_flux

       :class:`AdvectionDGFluxTerm <sfepy.terms.terms_dg.AdvectionDGFluxTerm>`
     - ``<opt_material>``, ``<material_advelo>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\partial{T_K}} \ul{n} \cdot \ul{f}^{*} (p_{in},
           p_{out})q

       where
           

       .. math::
            \ul{f}^{*}(p_{in}, p_{out}) = \ul{a} \frac{p_{in} +
           p_{out}}{2} + (1 - \alpha) \ul{n} C \frac{ p_{in} - p_{out}}{2},
   * - dw_dg_diffusion_flux

       :class:`DiffusionDGFluxTerm <sfepy.terms.terms_dg.DiffusionDGFluxTerm>`
     - ``<material_diffusion_tensor>``, ``<state>``, ``<virtual>``

       ``<material_diffusion_tensor>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\partial{T_K}} D \langle \nabla p \rangle [q] \mbox{
           , } \int_{\partial{T_K}} D \langle \nabla q \rangle [p]

       where
           

       .. math::
            \langle \nabla \phi \rangle = \frac{\nabla\phi_{in} +
           \nabla\phi_{out}}{2}

       .. math::
            [\phi] = \phi_{in} - \phi_{out}
   * - dw_dg_interior_penalty

       :class:`DiffusionInteriorPenaltyTerm <sfepy.terms.terms_dg.DiffusionInteriorPenaltyTerm>`
     - ``<material_diffusion_tensor>``, ``<material_Cw>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\partial{T_K}} \bar{D} C_w
           \frac{Ord^2}{d(\partial{T_K})}[p][q]

       where
           

       .. math::
            [\phi] = \phi_{in} - \phi_{out}
   * - dw_dg_nonlinear_laxfrie_flux

       :class:`NonlinearHyperbolicDGFluxTerm <sfepy.terms.terms_dg.NonlinearHyperbolicDGFluxTerm>`
     - ``<opt_material>``, ``<fun>``, ``<fun_d>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\partial{T_K}} \ul{n} \cdot f^{*} (p_{in}, p_{out})q

       where
           

       .. math::
            \ul{f}^{*}(p_{in}, p_{out}) = \frac{\ul{f}(p_{in}) +
           \ul{f}(p_{out})}{2} + (1 - \alpha) \ul{n} C \frac{ p_{in} -
           p_{out}}{2},
   * - dw_diffusion_coupling

       :class:`DiffusionCoupling <sfepy.terms.terms_diffusion.DiffusionCoupling>`
     - ``<material>``, ``<virtual>``, ``<state>``

       ``<material>``, ``<state>``, ``<virtual>``

       ``<material>``, ``<parameter_1>``, ``<parameter_2>``
     - .. math::
            \int_{\Omega} p K_{j} \nabla_j q \mbox{ , } \int_{\Omega}
           q K_{j} \nabla_j p
   * - dw_diffusion_r

       :class:`DiffusionRTerm <sfepy.terms.terms_diffusion.DiffusionRTerm>`
     - ``<material>``, ``<virtual>``
     - .. math::
            \int_{\Omega} K_{j} \nabla_j q
   * - ev_diffusion_velocity

       :class:`DiffusionVelocityTerm <sfepy.terms.terms_diffusion.DiffusionVelocityTerm>`
     - ``<material>``, ``<parameter>``
     - .. math::
            - \int_{\Omega} K_{ij} \nabla_j \bar{p}

       .. math::
            \mbox{vector for } K \from \Ical_h: - \int_{T_K} K_{ij}
           \nabla_j \bar{p} / \int_{T_K} 1

       .. math::
            - K_{ij} \nabla_j \bar{p}
   * - dw_diffusion

       :class:`DiffusionTerm <sfepy.terms.terms_diffusion.DiffusionTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``

       ``<material>``, ``<parameter_1>``, ``<parameter_2>``
     - .. math::
            \int_{\Omega} K_{ij} \nabla_i q \nabla_j p \mbox{ , }
           \int_{\Omega} K_{ij} \nabla_i \bar{p} \nabla_j r
   * - dw_div_grad

       :class:`DivGradTerm <sfepy.terms.terms_navier_stokes.DivGradTerm>`
     - ``<opt_material>``, ``<virtual>``, ``<state>``

       ``<opt_material>``, ``<parameter_1>``, ``<parameter_2>``
     - .. math::
            \int_{\Omega} \nu\ \nabla \ul{v} : \nabla \ul{u} \mbox{ ,
           } \int_{\Omega} \nu\ \nabla \ul{u} : \nabla \ul{w} \\
           \int_{\Omega} \nabla \ul{v} : \nabla \ul{u} \mbox{ , }
           \int_{\Omega} \nabla \ul{u} : \nabla \ul{w}
   * - dw_div

       :class:`DivOperatorTerm <sfepy.terms.terms_navier_stokes.DivOperatorTerm>`
     - ``<opt_material>``, ``<virtual>``
     - .. math::
            \int_{\Omega} \nabla \cdot \ul{v} \mbox { or }
           \int_{\Omega} c \nabla \cdot \ul{v}
   * - ev_div

       :class:`DivTerm <sfepy.terms.terms_navier_stokes.DivTerm>`
     - ``<parameter>``
     - .. math::
            \int_{\Omega} \nabla \cdot \ul{u}

       .. math::
            \mbox{vector for } K \from \Ical_h: \int_{T_K} \nabla
           \cdot \ul{u} / \int_{T_K} 1

       .. math::
            (\nabla \cdot \ul{u})|_{qp}
   * - dw_elastic_wave_cauchy

       :class:`ElasticWaveCauchyTerm <sfepy.terms.terms_elastic.ElasticWaveCauchyTerm>`
     - ``<material_1>``, ``<material_2>``, ``<virtual>``, ``<state>``

       ``<material_1>``, ``<material_2>``, ``<state>``, ``<virtual>``
     - .. math::
            \int_{\Omega} D_{ijkl}\ g_{ij}(\ul{v}) e_{kl}(\ul{u}) \;,
           \int_{\Omega} D_{ijkl}\ g_{ij}(\ul{u}) e_{kl}(\ul{v})
   * - dw_elastic_wave

       :class:`ElasticWaveTerm <sfepy.terms.terms_elastic.ElasticWaveTerm>`
     - ``<material_1>``, ``<material_2>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Omega} D_{ijkl}\ g_{ij}(\ul{v}) g_{kl}(\ul{u})
   * - dw_electric_source

       :class:`ElectricSourceTerm <sfepy.terms.terms_electric.ElectricSourceTerm>`
     - ``<material>``, ``<virtual>``, ``<parameter>``
     - .. math::
            \int_{\Omega} c s (\nabla \phi)^2
   * - ev_grad

       :class:`GradTerm <sfepy.terms.terms_navier_stokes.GradTerm>`
     - ``<parameter>``
     - .. math::
            \int_{\Omega} \nabla p \mbox{ or } \int_{\Omega} \nabla
           \ul{w}

       .. math::
            \mbox{vector for } K \from \Ical_h: \int_{T_K} \nabla p /
           \int_{T_K} 1 \mbox{ or } \int_{T_K} \nabla \ul{w} / \int_{T_K} 1

       .. math::
            (\nabla p)|_{qp} \mbox{ or } \nabla \ul{w}|_{qp}
   * - dw_jump

       :class:`SurfaceJumpTerm <sfepy.terms.terms_surface.SurfaceJumpTerm>`
     - ``<opt_material>``, ``<virtual>``, ``<state_1>``, ``<state_2>``
     - .. math::
            \int_{\Gamma} c\, q (p_1 - p_2)
   * - dw_laplace

       :class:`LaplaceTerm <sfepy.terms.terms_diffusion.LaplaceTerm>`
     - ``<opt_material>``, ``<virtual>``, ``<state>``

       ``<opt_material>``, ``<parameter_1>``, ``<parameter_2>``
     - .. math::
            \int_{\Omega} c \nabla q \cdot \nabla p \mbox{ , }
           \int_{\Omega} c \nabla \bar{p} \cdot \nabla r
   * - dw_lin_convect2

       :class:`LinearConvect2Term <sfepy.terms.terms_navier_stokes.LinearConvect2Term>`
     - ``<material>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Omega} ((\ul{b} \cdot \nabla) \ul{u}) \cdot \ul{v}

       .. math::
            ((\ul{b} \cdot \nabla) \ul{u})|_{qp}
   * - dw_lin_convect

       :class:`LinearConvectTerm <sfepy.terms.terms_navier_stokes.LinearConvectTerm>`
     - ``<virtual>``, ``<parameter>``, ``<state>``
     - .. math::
            \int_{\Omega} ((\ul{b} \cdot \nabla) \ul{u}) \cdot \ul{v}

       .. math::
            ((\ul{b} \cdot \nabla) \ul{u})|_{qp}
   * - dw_lin_elastic_iso

       :class:`LinearElasticIsotropicTerm <sfepy.terms.terms_elastic.LinearElasticIsotropicTerm>`
     - ``<material_1>``, ``<material_2>``, ``<virtual>``, ``<state>``

       ``<material_1>``, ``<material_2>``, ``<parameter_1>``, ``<parameter_2>``
     - .. math::
            \int_{\Omega} D_{ijkl}\ e_{ij}(\ul{v}) e_{kl}(\ul{u})
           \mbox{ with } D_{ijkl} = \mu (\delta_{ik} \delta_{jl}+\delta_{il}
           \delta_{jk}) + \lambda \ \delta_{ij} \delta_{kl}
   * - dw_lin_elastic

       :class:`LinearElasticTerm <sfepy.terms.terms_elastic.LinearElasticTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``

       ``<material>``, ``<parameter_1>``, ``<parameter_2>``
     - .. math::
            \int_{\Omega} D_{ijkl}\ e_{ij}(\ul{v}) e_{kl}(\ul{u})
   * - dw_lin_prestress

       :class:`LinearPrestressTerm <sfepy.terms.terms_elastic.LinearPrestressTerm>`
     - ``<material>``, ``<virtual>``

       ``<material>``, ``<parameter>``
     - .. math::
            \int_{\Omega} \sigma_{ij} e_{ij}(\ul{v})
   * - dw_lin_strain_fib

       :class:`LinearStrainFiberTerm <sfepy.terms.terms_elastic.LinearStrainFiberTerm>`
     - ``<material_1>``, ``<material_2>``, ``<virtual>``
     - .. math::
            \int_{\Omega} D_{ijkl} e_{ij}(\ul{v}) \left(d_k d_l\right)
   * - dw_non_penetration_p

       :class:`NonPenetrationPenaltyTerm <sfepy.terms.terms_constraints.NonPenetrationPenaltyTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Gamma} c (\ul{n} \cdot \ul{v}) (\ul{n} \cdot
           \ul{u})
   * - dw_non_penetration

       :class:`NonPenetrationTerm <sfepy.terms.terms_constraints.NonPenetrationTerm>`
     - ``<opt_material>``, ``<virtual>``, ``<state>``

       ``<opt_material>``, ``<state>``, ``<virtual>``
     - .. math::
            \int_{\Gamma} c \lambda \ul{n} \cdot \ul{v} \mbox{ , }
           \int_{\Gamma} c \hat\lambda \ul{n} \cdot \ul{u} \\ \int_{\Gamma}
           \lambda \ul{n} \cdot \ul{v} \mbox{ , } \int_{\Gamma} \hat\lambda
           \ul{n} \cdot \ul{u}
   * - dw_nonsym_elastic

       :class:`NonsymElasticTerm <sfepy.terms.terms_elastic.NonsymElasticTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``

       ``<material>``, ``<parameter_1>``, ``<parameter_2>``
     - .. math::
            \int_{\Omega} \ull{D} \nabla\ul{u} : \nabla\ul{v}
   * - dw_ns_dot_grad_s

       :class:`NonlinearScalarDotGradTerm <sfepy.terms.terms_dg.NonlinearScalarDotGradTerm>`
     - ``<fun>``, ``<fun_d>``, ``<virtual>``, ``<state>``

       ``<fun>``, ``<fun_d>``, ``<state>``, ``<virtual>``
     - .. math::
            \int_{\Omega} q \cdot \nabla \cdot \ul{f}(p) =
           \int_{\Omega} q \cdot \text{div} \ul{f}(p) \mbox{ , }
           \int_{\Omega} \ul{f}(p) \cdot \nabla q
   * - dw_piezo_coupling

       :class:`PiezoCouplingTerm <sfepy.terms.terms_piezo.PiezoCouplingTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``

       ``<material>``, ``<state>``, ``<virtual>``

       ``<material>``, ``<parameter_v>``, ``<parameter_s>``
     - .. math::
            \int_{\Omega} g_{kij}\ e_{ij}(\ul{v}) \nabla_k p \mbox{ ,
           } \int_{\Omega} g_{kij}\ e_{ij}(\ul{u}) \nabla_k q
   * - ev_piezo_strain

       :class:`PiezoStrainTerm <sfepy.terms.terms_piezo.PiezoStrainTerm>`
     - ``<material>``, ``<parameter>``
     - .. math::
            \int_{\Omega} g_{kij} e_{ij}(\ul{u})
   * - ev_piezo_stress

       :class:`PiezoStressTerm <sfepy.terms.terms_piezo.PiezoStressTerm>`
     - ``<material>``, ``<parameter>``
     - .. math::
            \int_{\Omega} g_{kij} \nabla_k p
   * - dw_point_load

       :class:`ConcentratedPointLoadTerm <sfepy.terms.terms_point.ConcentratedPointLoadTerm>`
     - ``<material>``, ``<virtual>``
     - .. math::
            \ul{f}^i = \ul{\bar f}^i \quad \forall \mbox{ FE node } i
           \mbox{ in a region }
   * - dw_point_lspring

       :class:`LinearPointSpringTerm <sfepy.terms.terms_point.LinearPointSpringTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``
     - .. math::
            \ul{f}^i = -k \ul{u}^i \quad \forall \mbox{ FE node } i
           \mbox{ in a region }
   * - dw_s_dot_grad_i_s

       :class:`ScalarDotGradIScalarTerm <sfepy.terms.terms_dot.ScalarDotGradIScalarTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``
     - .. math::
            Z^i = \int_{\Omega} q \nabla_i p
   * - dw_s_dot_mgrad_s

       :class:`ScalarDotMGradScalarTerm <sfepy.terms.terms_dot.ScalarDotMGradScalarTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``

       ``<material>``, ``<state>``, ``<virtual>``
     - .. math::
            \int_{\Omega} q \ul{y} \cdot \nabla p \mbox{ , }
           \int_{\Omega} p \ul{y} \cdot \nabla q
   * - dw_shell10x

       :class:`Shell10XTerm <sfepy.terms.terms_shells.Shell10XTerm>`
     - ``<material_d>``, ``<material_drill>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Omega} D_{ijkl}\ e_{ij}(\ul{v}) e_{kl}(\ul{u})
   * - dw_stokes_wave_div

       :class:`StokesWaveDivTerm <sfepy.terms.terms_navier_stokes.StokesWaveDivTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``

       ``<material>``, ``<state>``, ``<virtual>``
     - .. math::
            \int_{\Omega} (\ul{\kappa} \cdot \ul{v}) (\nabla \cdot
           \ul{u}) \;, \int_{\Omega} (\ul{\kappa} \cdot \ul{u}) (\nabla \cdot
           \ul{v})
   * - dw_stokes_wave

       :class:`StokesWaveTerm <sfepy.terms.terms_navier_stokes.StokesWaveTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Omega} (\ul{\kappa} \cdot \ul{v}) (\ul{\kappa}
           \cdot \ul{u})
   * - dw_stokes

       :class:`StokesTerm <sfepy.terms.terms_navier_stokes.StokesTerm>`
     - ``<opt_material>``, ``<virtual>``, ``<state>``

       ``<opt_material>``, ``<state>``, ``<virtual>``

       ``<opt_material>``, ``<parameter_v>``, ``<parameter_s>``
     - .. math::
            \int_{\Omega} p\ \nabla \cdot \ul{v} \mbox{ , }
           \int_{\Omega} q\ \nabla \cdot \ul{u} \mbox{ or } \int_{\Omega} c\
           p\ \nabla \cdot \ul{v} \mbox{ , } \int_{\Omega} c\ q\ \nabla \cdot
           \ul{u}
   * - d_sum_vals

       :class:`SumNodalValuesTerm <sfepy.terms.terms_basic.SumNodalValuesTerm>`
     - ``<parameter>``
     - 
   * - ev_surface_div

       :class:`SurfaceDivTerm <sfepy.terms.terms_navier_stokes.SurfaceDivTerm>`
     - ``<parameter>``
     - .. math::
            \int_{\Gamma} \nabla \cdot \ul{u}

       .. math::
            \mbox{vector for } K \from \Ical_h: \int_{T_K} \nabla
           \cdot \ul{u} / \int_{T_K} 1

       .. math::
            (\nabla \cdot \ul{u})|_{qp}
   * - dw_surface_dot

       :class:`DotProductSurfaceTerm <sfepy.terms.terms_dot.DotProductSurfaceTerm>`
     - ``<opt_material>``, ``<virtual>``, ``<state>``

       ``<opt_material>``, ``<parameter_1>``, ``<parameter_2>``
     - .. math::
            \int_\Gamma q p \mbox{ , } \int_\Gamma \ul{v} \cdot \ul{u}
           \mbox{ , } \int_\Gamma \ul{v} \cdot \ul{n} p \mbox{ , }
           \int_\Gamma q \ul{n} \cdot \ul{u} \mbox{ , } \int_\Gamma p r
           \mbox{ , } \int_\Gamma \ul{u} \cdot \ul{w} \mbox{ , } \int_\Gamma
           \ul{w} \cdot \ul{n} p \\ \int_\Gamma c q p \mbox{ , } \int_\Gamma
           c \ul{v} \cdot \ul{u} \mbox{ , } \int_\Gamma c p r \mbox{ , }
           \int_\Gamma c \ul{u} \cdot \ul{w} \\ \int_\Gamma \ul{v} \cdot
           \ull{M} \cdot \ul{u} \mbox{ , } \int_\Gamma \ul{u} \cdot \ull{M}
           \cdot \ul{w}
   * - d_surface_flux

       :class:`SurfaceFluxTerm <sfepy.terms.terms_diffusion.SurfaceFluxTerm>`
     - ``<material>``, ``<parameter>``
     - .. math::
            \int_{\Gamma} \ul{n} \cdot K_{ij} \nabla_j \bar{p}

       .. math::
            \mbox{vector for } K \from \Ical_h: \int_{T_K} \ul{n}
           \cdot K_{ij} \nabla_j \bar{p}\ / \int_{T_K} 1

       .. math::
            \mbox{vector for } K \from \Ical_h: \int_{T_K} \ul{n}
           \cdot K_{ij} \nabla_j \bar{p}
   * - dw_surface_flux

       :class:`SurfaceFluxOperatorTerm <sfepy.terms.terms_diffusion.SurfaceFluxOperatorTerm>`
     - ``<opt_material>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Gamma} q \ul{n} \cdot \ull{K} \cdot \nabla p
   * - ev_surface_grad

       :class:`SurfaceGradTerm <sfepy.terms.terms_navier_stokes.SurfaceGradTerm>`
     - ``<parameter>``
     - .. math::
            \int_{\Gamma} \nabla p \mbox{ or } \int_{\Gamma} \nabla
           \ul{w}

       .. math::
            \mbox{vector for } K \from \Ical_h: \int_{T_K} \nabla p /
           \int_{T_K} 1 \mbox{ or } \int_{T_K} \nabla \ul{w} / \int_{T_K} 1

       .. math::
            (\nabla p)|_{qp} \mbox{ or } \nabla \ul{w}|_{qp}
   * - ev_surface_integrate_mat

       :class:`IntegrateSurfaceMatTerm <sfepy.terms.terms_basic.IntegrateSurfaceMatTerm>`
     - ``<material>``, ``<parameter>``
     - .. math::
            \int_\Gamma m

       .. math::
            \mbox{vector for } K \from \Ical_h: \int_{T_K} m /
           \int_{T_K} 1

       .. math::
            m|_{qp}
   * - dw_surface_integrate

       :class:`IntegrateSurfaceOperatorTerm <sfepy.terms.terms_basic.IntegrateSurfaceOperatorTerm>`
     - ``<opt_material>``, ``<virtual>``
     - .. math::
            \int_{\Gamma} q \mbox{ or } \int_\Gamma c q
   * - ev_surface_integrate

       :class:`IntegrateSurfaceTerm <sfepy.terms.terms_basic.IntegrateSurfaceTerm>`
     - ``<opt_material>``, ``<parameter>``
     - .. math::
            \int_\Gamma y \mbox{ , } \int_\Gamma \ul{y} \mbox{ , }
           \int_\Gamma \ul{y} \cdot \ul{n} \\ \int_\Gamma c y \mbox{ , }
           \int_\Gamma c \ul{y} \mbox{ , } \int_\Gamma c \ul{y} \cdot \ul{n}
           \mbox{ flux }

       .. math::
            \mbox{vector for } K \from \Ical_h: \int_{T_K} y /
           \int_{T_K} 1 \mbox{ , } \int_{T_K} \ul{y} / \int_{T_K} 1 \mbox{ ,
           } \int_{T_K} (\ul{y} \cdot \ul{n}) / \int_{T_K} 1 \\ \mbox{vector
           for } K \from \Ical_h: \int_{T_K} c y / \int_{T_K} 1 \mbox{ , }
           \int_{T_K} c \ul{y} / \int_{T_K} 1 \mbox{ , } \int_{T_K} (c \ul{y}
           \cdot \ul{n}) / \int_{T_K} 1

       .. math::
            y|_{qp} \mbox{ , } \ul{y}|_{qp} \mbox{ , } (\ul{y} \cdot
           \ul{n})|_{qp} \mbox{ flux } \\ c y|_{qp} \mbox{ , } c \ul{y}|_{qp}
           \mbox{ , } (c \ul{y} \cdot \ul{n})|_{qp} \mbox{ flux }
   * - dw_surface_ltr

       :class:`LinearTractionTerm <sfepy.terms.terms_surface.LinearTractionTerm>`
     - ``<opt_material>``, ``<virtual>``

       ``<opt_material>``, ``<parameter>``
     - .. math::
            \int_{\Gamma} \ul{v} \cdot \ull{\sigma} \cdot \ul{n},
           \int_{\Gamma} \ul{v} \cdot \ul{n},
   * - d_surface_moment

       :class:`SurfaceMomentTerm <sfepy.terms.terms_basic.SurfaceMomentTerm>`
     - ``<material>``, ``<parameter>``
     - .. math::
            \int_{\Gamma} \ul{n} (\ul{x} - \ul{x}_0)
   * - dw_surface_ndot

       :class:`SufaceNormalDotTerm <sfepy.terms.terms_surface.SufaceNormalDotTerm>`
     - ``<material>``, ``<virtual>``

       ``<material>``, ``<parameter>``
     - .. math::
            \int_{\Gamma} q \ul{c} \cdot \ul{n}
   * - d_surface

       :class:`SurfaceTerm <sfepy.terms.terms_basic.SurfaceTerm>`
     - ``<parameter>``
     - .. math::
            \int_\Gamma 1
   * - dw_v_dot_grad_s

       :class:`VectorDotGradScalarTerm <sfepy.terms.terms_dot.VectorDotGradScalarTerm>`
     - ``<opt_material>``, ``<virtual>``, ``<state>``

       ``<opt_material>``, ``<state>``, ``<virtual>``

       ``<opt_material>``, ``<parameter_v>``, ``<parameter_s>``
     - .. math::
            \int_{\Omega} \ul{v} \cdot \nabla p \mbox{ , }
           \int_{\Omega} \ul{u} \cdot \nabla q \\ \int_{\Omega} c \ul{v}
           \cdot \nabla p \mbox{ , } \int_{\Omega} c \ul{u} \cdot \nabla q \\
           \int_{\Omega} \ul{v} \cdot (\ull{M} \nabla p) \mbox{ , }
           \int_{\Omega} \ul{u} \cdot (\ull{M} \nabla q)
   * - dw_vm_dot_s

       :class:`VectorDotScalarTerm <sfepy.terms.terms_dot.VectorDotScalarTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``

       ``<material>``, ``<state>``, ``<virtual>``

       ``<material>``, ``<parameter_v>``, ``<parameter_s>``
     - .. math::
            \int_{\Omega} \ul{v} \cdot \ul{m} p \mbox{ , }
           \int_{\Omega} \ul{u} \cdot \ul{m} q\\
   * - dw_volume_dot

       :class:`DotProductVolumeTerm <sfepy.terms.terms_dot.DotProductVolumeTerm>`
     - ``<opt_material>``, ``<virtual>``, ``<state>``

       ``<opt_material>``, ``<parameter_1>``, ``<parameter_2>``
     - .. math::
            \int_\Omega q p \mbox{ , } \int_\Omega \ul{v} \cdot \ul{u}
           \mbox{ , } \int_\Omega p r \mbox{ , } \int_\Omega \ul{u} \cdot
           \ul{w} \\ \int_\Omega c q p \mbox{ , } \int_\Omega c \ul{v} \cdot
           \ul{u} \mbox{ , } \int_\Omega c p r \mbox{ , } \int_\Omega c
           \ul{u} \cdot \ul{w} \\ \int_\Omega \ul{v} \cdot (\ull{M} \ul{u})
           \mbox{ , } \int_\Omega \ul{u} \cdot (\ull{M} \ul{w})
   * - ev_volume_integrate_mat

       :class:`IntegrateVolumeMatTerm <sfepy.terms.terms_basic.IntegrateVolumeMatTerm>`
     - ``<material>``, ``<parameter>``
     - .. math::
            \int_\Omega m

       .. math::
            \mbox{vector for } K \from \Ical_h: \int_{T_K} m /
           \int_{T_K} 1

       .. math::
            m|_{qp}
   * - dw_volume_integrate

       :class:`IntegrateVolumeOperatorTerm <sfepy.terms.terms_basic.IntegrateVolumeOperatorTerm>`
     - ``<opt_material>``, ``<virtual>``
     - .. math::
            \int_\Omega q \mbox{ or } \int_\Omega c q
   * - ev_volume_integrate

       :class:`IntegrateVolumeTerm <sfepy.terms.terms_basic.IntegrateVolumeTerm>`
     - ``<opt_material>``, ``<parameter>``
     - .. math::
            \int_\Omega y \mbox{ , } \int_\Omega \ul{y} \\ \int_\Omega
           c y \mbox{ , } \int_\Omega c \ul{y}

       .. math::
            \mbox{vector for } K \from \Ical_h: \int_{T_K} y /
           \int_{T_K} 1 \mbox{ , } \int_{T_K} \ul{y} / \int_{T_K} 1 \\
           \mbox{vector for } K \from \Ical_h: \int_{T_K} c y / \int_{T_K} 1
           \mbox{ , } \int_{T_K} c \ul{y} / \int_{T_K} 1

       .. math::
            y|_{qp} \mbox{ , } \ul{y}|_{qp} \\ c y|_{qp} \mbox{ , } c
           \ul{y}|_{qp}
   * - dw_volume_lvf

       :class:`LinearVolumeForceTerm <sfepy.terms.terms_volume.LinearVolumeForceTerm>`
     - ``<material>``, ``<virtual>``
     - .. math::
            \int_{\Omega} \ul{f} \cdot \ul{v} \mbox{ or }
           \int_{\Omega} f q
   * - d_volume_surface

       :class:`VolumeSurfaceTerm <sfepy.terms.terms_basic.VolumeSurfaceTerm>`
     - ``<parameter>``
     - .. math::
            1 / D \int_\Gamma \ul{x} \cdot \ul{n}
   * - d_volume

       :class:`VolumeTerm <sfepy.terms.terms_basic.VolumeTerm>`
     - ``<parameter>``
     - .. math::
            \int_\Omega 1
   * - dw_zero

       :class:`ZeroTerm <sfepy.terms.terms_basic.ZeroTerm>`
     - ``<virtual>``, ``<state>``
     - .. math::
            0

.. _term_table_sensitivity:

.. raw:: latex

   \newpage
Table of sensitivity terms
""""""""""""""""""""""""""

.. tabularcolumns:: |p{0.2\linewidth}|p{0.2\linewidth}|p{0.6\linewidth}|
.. list-table:: Sensitivity terms
   :widths: 20 20 60
   :header-rows: 1
   :class: longtable

   * - name/class
     - arguments
     - definition
   * - dw_adj_convect1

       :class:`AdjConvect1Term <sfepy.terms.terms_adj_navier_stokes.AdjConvect1Term>`
     - ``<virtual>``, ``<state>``, ``<parameter>``
     - .. math::
            \int_{\Omega} ((\ul{v} \cdot \nabla) \ul{u}) \cdot \ul{w}
   * - dw_adj_convect2

       :class:`AdjConvect2Term <sfepy.terms.terms_adj_navier_stokes.AdjConvect2Term>`
     - ``<virtual>``, ``<state>``, ``<parameter>``
     - .. math::
            \int_{\Omega} ((\ul{u} \cdot \nabla) \ul{v}) \cdot \ul{w}
   * - dw_adj_div_grad

       :class:`AdjDivGradTerm <sfepy.terms.terms_adj_navier_stokes.AdjDivGradTerm>`
     - ``<material_1>``, ``<material_2>``, ``<virtual>``, ``<parameter>``
     - .. math::
            w \delta_{u} \Psi(\ul{u}) \circ \ul{v}
   * - d_sd_convect

       :class:`SDConvectTerm <sfepy.terms.terms_adj_navier_stokes.SDConvectTerm>`
     - ``<parameter_u>``, ``<parameter_w>``, ``<parameter_mesh_velocity>``
     - .. math::
            \int_{\Omega} [ u_k \pdiff{u_i}{x_k} w_i (\nabla \cdot
           \Vcal) - u_k \pdiff{\Vcal_j}{x_k} \pdiff{u_i}{x_j} w_i ]
   * - d_sd_diffusion

       :class:`SDDiffusionTerm <sfepy.terms.terms_diffusion.SDDiffusionTerm>`
     - ``<material>``, ``<parameter_q>``, ``<parameter_p>``, ``<parameter_mesh_velocity>``
     - .. math::
            \int_{\Omega} \left[ (\dvg \ul{\Vcal}) K_{ij} \nabla_i q\,
           \nabla_j p - K_{ij} (\nabla_j \ul{\Vcal} \nabla q) \nabla_i p -
           K_{ij} \nabla_j q (\nabla_i \ul{\Vcal} \nabla p)\right]
   * - d_sd_div_grad

       :class:`SDDivGradTerm <sfepy.terms.terms_adj_navier_stokes.SDDivGradTerm>`
     - ``<material_1>``, ``<material_2>``, ``<parameter_u>``, ``<parameter_w>``, ``<parameter_mesh_velocity>``
     - .. math::
            w \nu \int_{\Omega} [ \pdiff{u_i}{x_k} \pdiff{w_i}{x_k}
           (\nabla \cdot \ul{\Vcal}) - \pdiff{\Vcal_j}{x_k} \pdiff{u_i}{x_j}
           \pdiff{w_i}{x_k} - \pdiff{u_i}{x_k} \pdiff{\Vcal_l}{x_k}
           \pdiff{w_i}{x_k} ]
   * - d_sd_div

       :class:`SDDivTerm <sfepy.terms.terms_adj_navier_stokes.SDDivTerm>`
     - ``<parameter_u>``, ``<parameter_p>``, ``<parameter_mesh_velocity>``
     - .. math::
            \int_{\Omega} p [ (\nabla \cdot \ul{w}) (\nabla \cdot
           \ul{\Vcal}) - \pdiff{\Vcal_k}{x_i} \pdiff{w_i}{x_k} ]
   * - d_sd_lin_elastic

       :class:`SDLinearElasticTerm <sfepy.terms.terms_elastic.SDLinearElasticTerm>`
     - ``<material>``, ``<parameter_w>``, ``<parameter_u>``, ``<parameter_mesh_velocity>``
     - .. math::
            \int_{\Omega} \hat{D}_{ijkl}\ e_{ij}(\ul{v})
           e_{kl}(\ul{u})

       .. math::
            \hat{D}_{ijkl} = D_{ijkl}(\nabla \cdot \ul{\Vcal}) -
           D_{ijkq}{\partial \Vcal_l \over \partial x_q} - D_{iqkl}{\partial
           \Vcal_j \over \partial x_q}
   * - d_sd_surface_integrate

       :class:`SDSufaceIntegrateTerm <sfepy.terms.terms_surface.SDSufaceIntegrateTerm>`
     - ``<parameter>``, ``<parameter_mesh_velocity>``
     - .. math::
            \int_{\Gamma} p \nabla \cdot \ul{\Vcal}
   * - d_sd_volume_dot

       :class:`SDDotVolumeTerm <sfepy.terms.terms_adj_navier_stokes.SDDotVolumeTerm>`
     - ``<parameter_1>``, ``<parameter_2>``, ``<parameter_mesh_velocity>``
     - .. math::
            \int_{\Omega} p q (\nabla \cdot \ul{\Vcal}) \mbox{ , }
           \int_{\Omega} (\ul{u} \cdot \ul{w}) (\nabla \cdot \ul{\Vcal})

.. _term_table_large deformation:

.. raw:: latex

   \newpage
Table of large deformation terms
""""""""""""""""""""""""""""""""

.. tabularcolumns:: |p{0.2\linewidth}|p{0.2\linewidth}|p{0.6\linewidth}|
.. list-table:: Large deformation terms
   :widths: 20 20 60
   :header-rows: 1
   :class: longtable

   * - name/class
     - arguments
     - definition
   * - dw_tl_bulk_active

       :class:`BulkActiveTLTerm <sfepy.terms.terms_hyperelastic_tl.BulkActiveTLTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})
   * - dw_tl_bulk_penalty

       :class:`BulkPenaltyTLTerm <sfepy.terms.terms_hyperelastic_tl.BulkPenaltyTLTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})
   * - dw_tl_bulk_pressure

       :class:`BulkPressureTLTerm <sfepy.terms.terms_hyperelastic_tl.BulkPressureTLTerm>`
     - ``<virtual>``, ``<state>``, ``<state_p>``
     - .. math::
            \int_{\Omega} S_{ij}(p) \delta E_{ij}(\ul{u};\ul{v})
   * - dw_tl_diffusion

       :class:`DiffusionTLTerm <sfepy.terms.terms_hyperelastic_tl.DiffusionTLTerm>`
     - ``<material_1>``, ``<material_2>``, ``<virtual>``, ``<state>``, ``<parameter>``
     - .. math::
            \int_{\Omega} \ull{K}(\ul{u}^{(n-1)}) : \pdiff{q}{\ul{X}}
           \pdiff{p}{\ul{X}}
   * - dw_tl_fib_a

       :class:`FibresActiveTLTerm <sfepy.terms.terms_fibres.FibresActiveTLTerm>`
     - ``<material_1>``, ``<material_2>``, ``<material_3>``, ``<material_4>``, ``<material_5>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})
   * - dw_tl_he_genyeoh

       :class:`GenYeohTLTerm <sfepy.terms.terms_hyperelastic_tl.GenYeohTLTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})
   * - dw_tl_he_mooney_rivlin

       :class:`MooneyRivlinTLTerm <sfepy.terms.terms_hyperelastic_tl.MooneyRivlinTLTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})
   * - dw_tl_he_neohook

       :class:`NeoHookeanTLTerm <sfepy.terms.terms_hyperelastic_tl.NeoHookeanTLTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})
   * - dw_tl_he_ogden

       :class:`OgdenTLTerm <sfepy.terms.terms_hyperelastic_tl.OgdenTLTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})
   * - dw_tl_membrane

       :class:`TLMembraneTerm <sfepy.terms.terms_membrane.TLMembraneTerm>`
     - ``<material_a1>``, ``<material_a2>``, ``<material_h0>``, ``<virtual>``, ``<state>``
     - 
   * - d_tl_surface_flux

       :class:`SurfaceFluxTLTerm <sfepy.terms.terms_hyperelastic_tl.SurfaceFluxTLTerm>`
     - ``<material_1>``, ``<material_2>``, ``<parameter_1>``, ``<parameter_2>``
     - .. math::
            \int_{\Gamma} \ul{\nu} \cdot \ull{K}(\ul{u}^{(n-1)})
           \pdiff{p}{\ul{X}}
   * - dw_tl_surface_traction

       :class:`SurfaceTractionTLTerm <sfepy.terms.terms_hyperelastic_tl.SurfaceTractionTLTerm>`
     - ``<opt_material>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Gamma} \ul{\nu} \cdot \ull{F}^{-1} \cdot
           \ull{\sigma} \cdot \ul{v} J
   * - d_tl_volume_surface

       :class:`VolumeSurfaceTLTerm <sfepy.terms.terms_hyperelastic_tl.VolumeSurfaceTLTerm>`
     - ``<parameter>``
     - .. math::
            1 / D \int_{\Gamma} \ul{\nu} \cdot \ull{F}^{-1} \cdot
           \ul{x} J
   * - dw_tl_volume

       :class:`VolumeTLTerm <sfepy.terms.terms_hyperelastic_tl.VolumeTLTerm>`
     - ``<virtual>``, ``<state>``
     - .. math::
            \begin{array}{l} \int_{\Omega} q J(\ul{u}) \\ \mbox{volume
           mode: vector for } K \from \Ical_h: \int_{T_K} J(\ul{u}) \\
           \mbox{rel\_volume mode: vector for } K \from \Ical_h: \int_{T_K}
           J(\ul{u}) / \int_{T_K} 1 \end{array}
   * - dw_ul_bulk_penalty

       :class:`BulkPenaltyULTerm <sfepy.terms.terms_hyperelastic_ul.BulkPenaltyULTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Omega} \mathcal{L}\tau_{ij}(\ul{u})
           e_{ij}(\delta\ul{v})/J
   * - dw_ul_bulk_pressure

       :class:`BulkPressureULTerm <sfepy.terms.terms_hyperelastic_ul.BulkPressureULTerm>`
     - ``<virtual>``, ``<state>``, ``<state_p>``
     - .. math::
            \int_{\Omega} \mathcal{L}\tau_{ij}(\ul{u})
           e_{ij}(\delta\ul{v})/J
   * - dw_ul_compressible

       :class:`CompressibilityULTerm <sfepy.terms.terms_hyperelastic_ul.CompressibilityULTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``, ``<parameter_u>``
     - .. math::
            \int_{\Omega} 1\over \gamma p \, q
   * - dw_ul_he_mooney_rivlin

       :class:`MooneyRivlinULTerm <sfepy.terms.terms_hyperelastic_ul.MooneyRivlinULTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Omega} \mathcal{L}\tau_{ij}(\ul{u})
           e_{ij}(\delta\ul{v})/J
   * - dw_ul_he_neohook

       :class:`NeoHookeanULTerm <sfepy.terms.terms_hyperelastic_ul.NeoHookeanULTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Omega} \mathcal{L}\tau_{ij}(\ul{u})
           e_{ij}(\delta\ul{v})/J
   * - dw_ul_volume

       :class:`VolumeULTerm <sfepy.terms.terms_hyperelastic_ul.VolumeULTerm>`
     - ``<virtual>``, ``<state>``
     - .. math::
            \begin{array}{l} \int_{\Omega} q J(\ul{u}) \\ \mbox{volume
           mode: vector for } K \from \Ical_h: \int_{T_K} J(\ul{u}) \\
           \mbox{rel\_volume mode: vector for } K \from \Ical_h: \int_{T_K}
           J(\ul{u}) / \int_{T_K} 1 \end{array}

.. _term_table_special:

.. raw:: latex

   \newpage
Table of special terms
""""""""""""""""""""""

.. tabularcolumns:: |p{0.2\linewidth}|p{0.2\linewidth}|p{0.6\linewidth}|
.. list-table:: Special terms
   :widths: 20 20 60
   :header-rows: 1
   :class: longtable

   * - name/class
     - arguments
     - definition
   * - dw_biot_eth

       :class:`BiotETHTerm <sfepy.terms.terms_biot.BiotETHTerm>`
     - ``<ts>``, ``<material_0>``, ``<material_1>``, ``<virtual>``, ``<state>``

       ``<ts>``, ``<material_0>``, ``<material_1>``, ``<state>``, ``<virtual>``
     - .. math::
            \begin{array}{l} \int_{\Omega} \left [\int_0^t
           \alpha_{ij}(t-\tau)\,p(\tau)) \difd{\tau} \right]\,e_{ij}(\ul{v})
           \mbox{ ,} \\ \int_{\Omega} \left [\int_0^t \alpha_{ij}(t-\tau)
           e_{kl}(\ul{u}(\tau)) \difd{\tau} \right] q \end{array}
   * - dw_biot_th

       :class:`BiotTHTerm <sfepy.terms.terms_biot.BiotTHTerm>`
     - ``<ts>``, ``<material>``, ``<virtual>``, ``<state>``

       ``<ts>``, ``<material>``, ``<state>``, ``<virtual>``
     - .. math::
            \begin{array}{l} \int_{\Omega} \left [\int_0^t
           \alpha_{ij}(t-\tau)\,p(\tau)) \difd{\tau} \right]\,e_{ij}(\ul{v})
           \mbox{ ,} \\ \int_{\Omega} \left [\int_0^t \alpha_{ij}(t-\tau)
           e_{kl}(\ul{u}(\tau)) \difd{\tau} \right] q \end{array}
   * - ev_cauchy_stress_eth

       :class:`CauchyStressETHTerm <sfepy.terms.terms_elastic.CauchyStressETHTerm>`
     - ``<ts>``, ``<material_0>``, ``<material_1>``, ``<parameter>``
     - .. math::
            \int_{\Omega} \int_0^t
           \Hcal_{ijkl}(t-\tau)\,e_{kl}(\ul{w}(\tau)) \difd{\tau}

       .. math::
            \mbox{vector for } K \from \Ical_h: \int_{T_K} \int_0^t
           \Hcal_{ijkl}(t-\tau)\,e_{kl}(\ul{w}(\tau)) \difd{\tau} /
           \int_{T_K} 1

       .. math::
            \int_0^t \Hcal_{ijkl}(t-\tau)\,e_{kl}(\ul{w}(\tau))
           \difd{\tau}|_{qp}
   * - ev_cauchy_stress_th

       :class:`CauchyStressTHTerm <sfepy.terms.terms_elastic.CauchyStressTHTerm>`
     - ``<ts>``, ``<material>``, ``<parameter>``
     - .. math::
            \int_{\Omega} \int_0^t
           \Hcal_{ijkl}(t-\tau)\,e_{kl}(\ul{w}(\tau)) \difd{\tau}

       .. math::
            \mbox{vector for } K \from \Ical_h: \int_{T_K} \int_0^t
           \Hcal_{ijkl}(t-\tau)\,e_{kl}(\ul{w}(\tau)) \difd{\tau} /
           \int_{T_K} 1

       .. math::
            \int_0^t \Hcal_{ijkl}(t-\tau)\,e_{kl}(\ul{w}(\tau))
           \difd{\tau}|_{qp}
   * - dw_lin_elastic_eth

       :class:`LinearElasticETHTerm <sfepy.terms.terms_elastic.LinearElasticETHTerm>`
     - ``<ts>``, ``<material_0>``, ``<material_1>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Omega} \left [\int_0^t
           \Hcal_{ijkl}(t-\tau)\,e_{kl}(\ul{u}(\tau)) \difd{\tau}
           \right]\,e_{ij}(\ul{v})
   * - dw_lin_elastic_th

       :class:`LinearElasticTHTerm <sfepy.terms.terms_elastic.LinearElasticTHTerm>`
     - ``<ts>``, ``<material>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_{\Omega} \left [\int_0^t
           \Hcal_{ijkl}(t-\tau)\,e_{kl}(\ul{u}(\tau)) \difd{\tau}
           \right]\,e_{ij}(\ul{v})
   * - dw_of_ns_surf_min_d_press_diff

       :class:`NSOFSurfMinDPressDiffTerm <sfepy.terms.terms_adj_navier_stokes.NSOFSurfMinDPressDiffTerm>`
     - ``<material>``, ``<virtual>``
     - .. math::
            w \delta_{p} \Psi(p) \circ q
   * - d_of_ns_surf_min_d_press

       :class:`NSOFSurfMinDPressTerm <sfepy.terms.terms_adj_navier_stokes.NSOFSurfMinDPressTerm>`
     - ``<material_1>``, ``<material_2>``, ``<parameter>``
     - .. math::
            \delta \Psi(p) = \delta \left( \int_{\Gamma_{in}}p -
           \int_{\Gamma_{out}}bpress \right)
   * - d_sd_st_grad_div

       :class:`SDGradDivStabilizationTerm <sfepy.terms.terms_adj_navier_stokes.SDGradDivStabilizationTerm>`
     - ``<material>``, ``<parameter_u>``, ``<parameter_w>``, ``<parameter_mesh_velocity>``
     - .. math::
            \gamma \int_{\Omega} [ (\nabla \cdot \ul{u}) (\nabla \cdot
           \ul{w}) (\nabla \cdot \ul{\Vcal}) - \pdiff{u_i}{x_k}
           \pdiff{\Vcal_k}{x_i} (\nabla \cdot \ul{w}) - (\nabla \cdot \ul{u})
           \pdiff{w_i}{x_k} \pdiff{\Vcal_k}{x_i} ]
   * - d_sd_st_pspg_c

       :class:`SDPSPGCStabilizationTerm <sfepy.terms.terms_adj_navier_stokes.SDPSPGCStabilizationTerm>`
     - ``<material>``, ``<parameter_b>``, ``<parameter_u>``, ``<parameter_r>``, ``<parameter_mesh_velocity>``
     - .. math::
            \sum_{K \in \Ical_h}\int_{T_K} \delta_K\ [ \pdiff{r}{x_i}
           (\ul{b} \cdot \nabla u_i) (\nabla \cdot \Vcal) - \pdiff{r}{x_k}
           \pdiff{\Vcal_k}{x_i} (\ul{b} \cdot \nabla u_i) - \pdiff{r}{x_k}
           (\ul{b} \cdot \nabla \Vcal_k) \pdiff{u_i}{x_k} ]
   * - d_sd_st_pspg_p

       :class:`SDPSPGPStabilizationTerm <sfepy.terms.terms_adj_navier_stokes.SDPSPGPStabilizationTerm>`
     - ``<material>``, ``<parameter_r>``, ``<parameter_p>``, ``<parameter_mesh_velocity>``
     - .. math::
            \sum_{K \in \Ical_h}\int_{T_K} \tau_K\ [ (\nabla r \cdot
           \nabla p) (\nabla \cdot \Vcal) - \pdiff{r}{x_k} (\nabla \Vcal_k
           \cdot \nabla p) - (\nabla r \cdot \nabla \Vcal_k) \pdiff{p}{x_k} ]
   * - d_sd_st_supg_c

       :class:`SDSUPGCStabilizationTerm <sfepy.terms.terms_adj_navier_stokes.SDSUPGCStabilizationTerm>`
     - ``<material>``, ``<parameter_b>``, ``<parameter_u>``, ``<parameter_w>``, ``<parameter_mesh_velocity>``
     - .. math::
            \sum_{K \in \Ical_h}\int_{T_K} \delta_K\ [ (\ul{b} \cdot
           \nabla u_k) (\ul{b} \cdot \nabla w_k) (\nabla \cdot \Vcal) -
           (\ul{b} \cdot \nabla \Vcal_i) \pdiff{u_k}{x_i} (\ul{b} \cdot
           \nabla w_k) - (\ul{u} \cdot \nabla u_k) (\ul{b} \cdot \nabla
           \Vcal_i) \pdiff{w_k}{x_i} ]
   * - dw_st_adj1_supg_p

       :class:`SUPGPAdj1StabilizationTerm <sfepy.terms.terms_adj_navier_stokes.SUPGPAdj1StabilizationTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``, ``<parameter>``
     - .. math::
            \sum_{K \in \Ical_h}\int_{T_K} \delta_K\ \nabla p (\ul{v}
           \cdot \nabla \ul{w})
   * - dw_st_adj2_supg_p

       :class:`SUPGPAdj2StabilizationTerm <sfepy.terms.terms_adj_navier_stokes.SUPGPAdj2StabilizationTerm>`
     - ``<material>``, ``<virtual>``, ``<parameter>``, ``<state>``
     - .. math::
            \sum_{K \in \Ical_h}\int_{T_K} \tau_K\ \nabla r (\ul{v}
           \cdot \nabla \ul{u})
   * - dw_st_adj_supg_c

       :class:`SUPGCAdjStabilizationTerm <sfepy.terms.terms_adj_navier_stokes.SUPGCAdjStabilizationTerm>`
     - ``<material>``, ``<virtual>``, ``<parameter>``, ``<state>``
     - .. math::
            \sum_{K \in \Ical_h}\int_{T_K} \delta_K\ [ ((\ul{v} \cdot
           \nabla) \ul{u}) ((\ul{u} \cdot \nabla) \ul{w}) + ((\ul{u} \cdot
           \nabla) \ul{u}) ((\ul{v} \cdot \nabla) \ul{w}) ]
   * - dw_st_grad_div

       :class:`GradDivStabilizationTerm <sfepy.terms.terms_navier_stokes.GradDivStabilizationTerm>`
     - ``<material>``, ``<virtual>``, ``<state>``
     - .. math::
            \gamma \int_{\Omega} (\nabla\cdot\ul{u}) \cdot
           (\nabla\cdot\ul{v})
   * - dw_st_pspg_c

       :class:`PSPGCStabilizationTerm <sfepy.terms.terms_navier_stokes.PSPGCStabilizationTerm>`
     - ``<material>``, ``<virtual>``, ``<parameter>``, ``<state>``
     - .. math::
            \sum_{K \in \Ical_h}\int_{T_K} \tau_K\ ((\ul{b} \cdot
           \nabla) \ul{u}) \cdot \nabla q
   * - dw_st_pspg_p

       :class:`PSPGPStabilizationTerm <sfepy.terms.terms_navier_stokes.PSPGPStabilizationTerm>`
     - ``<opt_material>``, ``<virtual>``, ``<state>``

       ``<opt_material>``, ``<parameter_1>``, ``<parameter_2>``
     - .. math::
            \sum_{K \in \Ical_h}\int_{T_K} \tau_K\ \nabla p \cdot
           \nabla q
   * - dw_st_supg_c

       :class:`SUPGCStabilizationTerm <sfepy.terms.terms_navier_stokes.SUPGCStabilizationTerm>`
     - ``<material>``, ``<virtual>``, ``<parameter>``, ``<state>``
     - .. math::
            \sum_{K \in \Ical_h}\int_{T_K} \delta_K\ ((\ul{b} \cdot
           \nabla) \ul{u})\cdot ((\ul{b} \cdot \nabla) \ul{v})
   * - dw_st_supg_p

       :class:`SUPGPStabilizationTerm <sfepy.terms.terms_navier_stokes.SUPGPStabilizationTerm>`
     - ``<material>``, ``<virtual>``, ``<parameter>``, ``<state>``
     - .. math::
            \sum_{K \in \Ical_h}\int_{T_K} \delta_K\ \nabla p\cdot
           ((\ul{b} \cdot \nabla) \ul{v})
   * - dw_volume_dot_w_scalar_eth

       :class:`DotSProductVolumeOperatorWETHTerm <sfepy.terms.terms_dot.DotSProductVolumeOperatorWETHTerm>`
     - ``<ts>``, ``<material_0>``, ``<material_1>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_\Omega \left [\int_0^t \Gcal(t-\tau) p(\tau)
           \difd{\tau} \right] q
   * - dw_volume_dot_w_scalar_th

       :class:`DotSProductVolumeOperatorWTHTerm <sfepy.terms.terms_dot.DotSProductVolumeOperatorWTHTerm>`
     - ``<ts>``, ``<material>``, ``<virtual>``, ``<state>``
     - .. math::
            \int_\Omega \left [\int_0^t \Gcal(t-\tau) p(\tau)
           \difd{\tau} \right] q


.. raw:: latex

   \newpage
