From c2582424b5617a27e667ef79cdff84e2f7a42ecb Mon Sep 17 00:00:00 2001 From: bangerth Date: Tue, 7 Feb 2012 08:42:48 +0000 Subject: [PATCH] Add one future direction. git-svn-id: https://svn.dealii.org/trunk@25000 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-43/doc/results.dox | 12 ++++++++++++ 1 file changed, 12 insertions(+) diff --git a/deal.II/examples/step-43/doc/results.dox b/deal.II/examples/step-43/doc/results.dox index fc5ee916ff..f5111ed290 100644 --- a/deal.II/examples/step-43/doc/results.dox +++ b/deal.II/examples/step-43/doc/results.dox @@ -69,3 +69,15 @@ between multiple phases also play a role in oil reservoir modeling when considering controlled burns of oil in the reservoir to raise pressure and temperature. These are much more complex problems, though, and left for future projects. + +Finally, from a mathematical perspective, we have derived the +criterion for re-computing the velocity/pressure solution at a given +time step under the assumption that we want to compare the solution we +would get at the current time step with that computed the last time we +actually solved this system. However, in the program, whenever we did +not re-compute the solution, we didn't just use the previously +computed solution but instead extrapolated from the previous two times +we solved the system. Consequently, the criterion was pessimistically +stated: what we should really compare is the solution we would get at +the current time step with the extrapolated one. Re-stating the +theorem in this regard is left as an exercise. -- 2.39.5