From: bangerth Date: Sun, 2 Jan 2011 23:10:00 +0000 (+0000) Subject: Finish introduction. X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=6e686e86857abb2c13be7f4c9b806364ffff45b7;p=dealii-svn.git Finish introduction. git-svn-id: https://svn.dealii.org/trunk@23097 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 bef01c5927..4d5e45da29 100644 --- a/deal.II/examples/step-38/doc/intro.dox +++ b/deal.II/examples/step-38/doc/intro.dox @@ -295,15 +295,32 @@ 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 +n\right]\nabla u$ to the function VectorTools::integrate_difference +(introduced first in step-7), which we will do by implementing the function Solution::gradient in the program below.

Implementation

+If you've read through step-4 and understand the discussion above of how +solution and right hand side correspond to each other, you will be immediately +familiar with this program as well. In fact, there are only two things that +are of significance: -Mapping objects +- The way we generate the mesh that triangulates the computational domain. +- The way we use Mapping objects to describe that the domain on which we solve + the partial differential equation is not planar but in fact curved. +Mapping objects were already introduced in step-10 and step-11 and as +explained there, there is usually not a whole lot you have to know about how +they work as long as you have a working description of how the boundary +looks. In essence, we will simply declare an appropriate object of type +MappingQ that will automatically obtain the boundary description from the +Triangulation. The mapping object will then be passed to the appropriate +functions, and we will get a boundary description for half circles or half +spheres that is pre-defined in the library. +The rest of the program follows closely step-4 and, as far as computing the +error, step-7.