]> https://gitweb.dealii.org/ - dealii-svn.git/commitdiff
Add one future direction.
authorbangerth <bangerth@0785d39b-7218-0410-832d-ea1e28bc413d>
Tue, 7 Feb 2012 08:42:48 +0000 (08:42 +0000)
committerbangerth <bangerth@0785d39b-7218-0410-832d-ea1e28bc413d>
Tue, 7 Feb 2012 08:42:48 +0000 (08:42 +0000)
git-svn-id: https://svn.dealii.org/trunk@25000 0785d39b-7218-0410-832d-ea1e28bc413d

deal.II/examples/step-43/doc/results.dox

index fc5ee916ffa1ae8a2746eac467e44342291ff5a9..f5111ed2900ceb0611d489758e05c96ea89ea1c9 100644 (file)
@@ -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.

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