From: Wolfgang Bangerth Date: Sun, 2 Jan 2011 22:58:23 +0000 (+0000) Subject: Discuss the issues with the exact solution and the remainder of the testcase. X-Git-Tag: v8.0.0~4563 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=6493ecf78a75f73251df6d9aa977e41071db65ad;p=dealii.git Discuss the issues with the exact solution and the remainder of the testcase. git-svn-id: https://svn.dealii.org/trunk@23096 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-38/doc/intro.dox b/deal.II/examples/step-38/doc/intro.dox index 332ee93fd5..bef01c5927 100644 --- a/deal.II/examples/step-38/doc/intro.dox +++ b/deal.II/examples/step-38/doc/intro.dox @@ -127,13 +127,177 @@ domain is obviously also essential. We produce one test case for a 2d problem and another one for 3d: -- In 2d, let's choose as domain a half circle. On this domain, we choose the - function $u(\mathbf x)=-2x_1x_2$ as the solution. + + +In the program, we will also compute the $H^1$ seminorm error of the +solution. Since the solution function and its numerical approximation are only +defined on the manifold, the obvious definition of this error functional is +$| e |_{H^1} = \left( \int_\Omega | \left[\mathbf n \otimes \mathbf +n\right]\nabla (u-u_h) |^2 \right)^{1/2}$. This requires us to provide the +tangential gradient $\left[\mathbf n \otimes \mathbf +n\right]\nabla u$ to the function VectorTools::integrate_difference, which we +will do by implementing the function Solution::gradient in the +program below.

Implementation