From bf75efba4b9d11be165afd52b7e006298e11b9ca Mon Sep 17 00:00:00 2001 From: bangerth Date: Sat, 9 Sep 2006 20:18:00 +0000 Subject: [PATCH] Refer to the condition as the CFL condition. git-svn-id: https://svn.dealii.org/trunk@13873 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-23/doc/intro.dox | 17 +++++++++-------- 1 file changed, 9 insertions(+), 8 deletions(-) diff --git a/deal.II/examples/step-23/doc/intro.dox b/deal.II/examples/step-23/doc/intro.dox index 11072ca942..1fca1cf284 100644 --- a/deal.II/examples/step-23/doc/intro.dox +++ b/deal.II/examples/step-23/doc/intro.dox @@ -366,14 +366,15 @@ $\theta>0$, our solutions will not be numerically stable if we violate this restriction. Implicit schemes do not have this restriction for stability, but they become inaccurate if the time step is too large. -This condition was first recognized by Courant, Friedrichs, and Levy — in -1943, long before computers become available for numerical computations! In -the program, we will refine a square $[-1,1]$ seven times uniformly, giving a -mesh size of $h=\frac 1{64}$, which is what we set the time step to. The fact -that we set the time step and mesh size individually in two different places -is error prone: it is too easy to refine the mesh once more but forget to also -adjust the time step. @ref step_24 "step-24" shows a better way how to keep -these things in synch. +This condition was first recognized by Courant, Friedrichs, and Levy — +in 1943, long before computers become available for numerical computations! +Consequently, the condition on the time step is most frequently just referred +to as the CFL condition. In the program, we will refine a square +$[-1,1]$ seven times uniformly, giving a mesh size of $h=\frac 1{64}$, which +is what we set the time step to. The fact that we set the time step and mesh +size individually in two different places is error prone: it is too easy to +refine the mesh once more but forget to also adjust the time step. @ref +step_24 "step-24" shows a better way how to keep these things in synch.

The testcase

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