From 98e0c820b331391d2e2dd6222b5d0589a426d831 Mon Sep 17 00:00:00 2001 From: bangerth Date: Wed, 15 Nov 2006 05:37:10 +0000 Subject: [PATCH] Fix energy, again. git-svn-id: https://svn.dealii.org/trunk@14194 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-25/doc/results.dox | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/deal.II/examples/step-25/doc/results.dox b/deal.II/examples/step-25/doc/results.dox index 9e5c1183bb..8def52582a 100644 --- a/deal.II/examples/step-25/doc/results.dox +++ b/deal.II/examples/step-25/doc/results.dox @@ -122,8 +122,11 @@ is defined as @f[ E(t) = \frac 12 \int_\Omega \left(\frac{\partial u}{\partial t}\right)^2 - + \left(\nabla u\right)^2 - 2 \cos u \; dx. + + \left(\nabla u\right)^2 + 2 (1-\cos u) \; dx. @f] +(The constant $2$ appears in the formula to ensure that all contributions to +the energy are positive, and so that decaying solutions have finite energy on +unbounded domains.) Beyond this, clearly, adaptivity (i.e. time-adaptive grids) would be of interest to problems like these. Their complexity leads us to leave this out -- 2.39.5