From: bangerth Date: Mon, 11 Jun 2012 10:14:03 +0000 (+0000) Subject: Comment on the refinement criterion. X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=11af2c56e7143582dee1f1c80d9d51945c38e82f;p=dealii-svn.git Comment on the refinement criterion. git-svn-id: https://svn.dealii.org/trunk@25621 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-43/doc/intro.dox b/deal.II/examples/step-43/doc/intro.dox index 998e3f35a4..f0532e4bd1 100644 --- a/deal.II/examples/step-43/doc/intro.dox +++ b/deal.II/examples/step-43/doc/intro.dox @@ -308,7 +308,10 @@ computed by where $\nabla S_h(\mathbf x_K)$ is the gradient of the discrete saturation variable evaluated at the center $\mathbf x_K$ of cell $K$. This approach is analogous to ones frequently used in compressible flow problems, where density -gradients are used to indicate refinement. +gradients are used to indicate refinement. That said, as we will +discuss at the end of the results section, this turns +out to not be a very useful criterion since it leads to refinement basically +everywhere. We only show it here for illustrative purposes.

Linear system and its preconditioning.

diff --git a/deal.II/examples/step-43/doc/results.dox b/deal.II/examples/step-43/doc/results.dox index cbc8d7dac4..f07f8e2fc5 100644 --- a/deal.II/examples/step-43/doc/results.dox +++ b/deal.II/examples/step-43/doc/results.dox @@ -99,3 +99,13 @@ recomputed is appropriate; one may, for example, suggest that it is also important to decide whether (and by how much) a wrong velocity field in fact affects the solution of the saturation equation. This would then naturally lead to a sensitivity analysis. + +From an algorithmic viewpoint, we have here used a criterion for refinement +that is often used in engineering, namely by looking at the gradient of +the solution. However, if you inspect the solution, you will find that +it quickly leads to refinement almost everywhere, even in regions where it +is clearly not necessary: frequently used therefore does not need to imply +that it is a useful criterion to begin with. On the other hand, replacing +this criterion by a different and better one should not be very difficult. +For example, the KellyErrorEstimator class used in many other programs +should certainly be applicable to the current problem as well.