step-38.h

    triangulation.set_boundary (0);                            /* ** */
    GridTools::transform (&warp<spacedim>, triangulation);     /* ** */
    std::ofstream x("x"), y("y");
    GridOut().write_gnuplot (volume_mesh, x);
    GridOut().write_gnuplot (triangulation, y);
  }

  std::cout << "Surface mesh has " << triangulation.n_active_cells()
            << " cells."
            << std::endl;

  ...
@endcode

Note that the only essential addition has been the three lines marked with
asterisks. It is worth pointing out one other thing here, though: because we
detach the manifold description from the surface mesh, whenever we use a
mapping object in the rest of the program, it has no curves boundary
description to go on any more. Rather, it will have to use the implicit,
StraightBoundary class that is used on all parts of the boundary not
explicitly assigned a different manifold object. Consequently, whether we use
MappingQ(2), MappingQ(15) or MappingQ1, each cell of our mesh will be mapped
using a bilinear approximation.

All these drawbacks aside, the resulting pictures are still pretty. The only
other differences to what's in @ref step_38 "step-38" is that we changed the right hand side
to @f$f(\mathbf x)=\sin x_3@f$ and the boundary values (through the
<code>Solution</code> class) to @f$u(\mathbf x)|_{\partial\Omega}=\cos x_3@f$. Of
course, we now non longer know the exact solution, so the computation of the
error at the end of <code>LaplaceBeltrami::run</code> will yield a meaningless
number.
<a name="PlainProg"></a>
<h1> The plain program</h1>
@include "step-38.cc"
 */