From 6c191896a572a5be82fe87d89e45dc2d22829937 Mon Sep 17 00:00:00 2001 From: bangerth Date: Mon, 31 Oct 2011 20:27:20 +0000 Subject: [PATCH] Link to step-30. git-svn-id: https://svn.dealii.org/trunk@24713 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-12/doc/results.dox | 9 ++++++++- 1 file changed, 8 insertions(+), 1 deletion(-) diff --git a/deal.II/examples/step-12/doc/results.dox b/deal.II/examples/step-12/doc/results.dox index 02998aae3f..ec60b8a491 100644 --- a/deal.II/examples/step-12/doc/results.dox +++ b/deal.II/examples/step-12/doc/results.dox @@ -80,7 +80,7 @@ avenue for further extensions would be to confirm the order of convergence for this program. In the current case, the solution is non-smooth, and so we can not expect to get a particularly high order of convergence, even if we used higher order elements. But even if the -solution is smooth, the equation is not elliptic and so it is not +solution is smooth, the equation is not elliptic and so it is not immediately clear that we should obtain a convergence order that equals that of the optimal interpolation estimates (i.e. for example that we would get $h^3$ convergence in the $L^2$ norm by using @@ -97,3 +97,10 @@ uniformly refined meshes, one can construct so-called Peterson meshes on which the worse theoretical bound is actually attained. This should be relatively simple to verify, for example using the VectorTools::integrate_difference function. + +A different direction is to observe that the solution of transport problems +often has discontinuities and that therefore a mesh in which we bisect +every cell in every coordinate direction may not be optimal. Rather, a better +strategy would be to only cut cells in the direction parallel to the +discontinuity. This is called anisotropic mesh refinement and is the +subject of step-30. -- 2.39.5