Modernize step-14

[kronbichler]

I've been using the step-14 tutorial program for teaching. Working with it, I found several components where I think we have much better solutions now, so we might think about replacing them. Let me list the items I would change:

• The evaluation of a point value should replace https://github.com/dealii/dealii/blob/69c845d78c33419aa6b1f3037930709ed4ca79da/examples/step-14/step-14.cc#LL130C1-L143C1 by VectorTools::point_value with the comment that there are even more efficient strategies with some GridTools::Cache or RemotePointEvaluation - maybe also directly show VectorTools::point_values().
• Similarly, for

  dealii/examples/step-14/step-14.cc

  Lines 195 to 198 in 69c845d

  	void PointXDerivativeEvaluation<dim>::operator()(
  	const DoFHandler<dim> &dof_handler,
  	const Vector<double> & solution) const
  	{

  we should use modern facilities, such as VectorTools::point_gradients().
• The computation of the right-hand side,

  dealii/examples/step-14/step-14.cc

  Lines 1432 to 1450 in 69c845d

  	PointValueEvaluation<dim>::assemble_rhs(const DoFHandler<dim> &dof_handler,
  	Vector<double> & rhs) const
  	{
  	// So, first set everything to zeros...
  	rhs.reinit(dof_handler.n_dofs());
  	// ...then loop over cells and find the evaluation point among the
  	// vertices (or very close to a vertex, which may happen due to floating
  	// point round-off):
  	for (const auto &cell : dof_handler.active_cell_iterators())
  	for (const auto vertex : cell->vertex_indices())
  	if (cell->vertex(vertex).distance(evaluation_point) <
  	cell->diameter() * 1e-8)
  	{
  	// Ok, found, so set corresponding entry, and leave function
  	// since we are finished:
  	rhs(cell->vertex_dof_index(vertex, 0)) = 1;
  	return;
  	}

  we could use FEPointEvaluation in conjunction with find_active_cell_around_point.

Note that there might be some educational value in the old way, but I think one stumbles over these things so often that one should not teach a way that we would not recommend at all. Besides these rather isolated bullet points, there might be more things to consider, such as computing the interface jumps with mesh_loop or similar facilities, but I do not consider myself enough expert to do that. I would personally do things in yet another way via FEEvaluation/FEFaceEvaluation, but that is a personal flavor that should not guide the tutorial here.

Any other ideas we should collect? Or opinions that some of the things should not be changed?