From 488b3c33ec7f72a80d32354b5d5f695349a6d653 Mon Sep 17 00:00:00 2001 From: wolf Date: Thu, 6 Jan 2000 15:52:29 +0000 Subject: [PATCH] Finish step-6 and modify foot of all pages to allow return to step-by-step index rather than tutorial index. git-svn-id: https://svn.dealii.org/trunk@2162 0785d39b-7218-0410-832d-ea1e28bc413d --- .../chapter-2.step-by-step/step-6.intro | 39 +++++++++++++++++++ .../chapter-2.step-by-step/step-by-step.foot | 2 +- .../tutorial/chapter-2.step-by-step/toc.html | 3 +- 3 files changed, 42 insertions(+), 2 deletions(-) diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-6.intro b/deal.II/doc/tutorial/chapter-2.step-by-step/step-6.intro index a3108dcb4c..89dbe461bc 100644 --- a/deal.II/doc/tutorial/chapter-2.step-by-step/step-6.intro +++ b/deal.II/doc/tutorial/chapter-2.step-by-step/step-6.intro @@ -2,4 +2,43 @@

Introduction

+The main emphasis in this example is the handling of locally refined +grids. In our approach to adaptivity, we use grids of which +neighboring cells may be refined a different number of times, and then +there result nodes on the interfaces of cells which belong to one +side, but are unbalanced on the other. We call these ``hanging nodes''. +

+ +

+To guarantee that the global solution is continuous at these nodes as +well, we have to state some additional constraints on the values of +the solution at these nodes, and we will show how to obtain these +constraints and how to use them in the solution of the linear system +of equations. +

+ +

+The locally refined grids are produced using an error estimator class +which estimates the energy error with respect to the Laplace +operator. This error estimator, although developed for Laplace's +equation has proven to be a suitable tool to generate locally refined +meshes for a wide range of equations, not restricted to elliptic +problems. Although it will create non-optimal meshes for other +equations, it is often a good way to quickly produce meshes that are +well adapted to the features of solutions, such as regions of great +variation or discontinuities. Although the error estimator (and its +implementation in the deal.II library) is capable of handling variable +coefficients in the equation, we will not use this feature since we +are only interested in a quick and simple way to generate locally +refined grids. +

+ +

+Since the concepts used for locally refined grids are so important, +we do not show much additional new stuff in this example. There will +be large regions in the code that are unaltered from the previous +example and which we will not comment on further. The only other new +thing is a method to catch exceptions in the ``main'' function in +order to output some information in case the program crashes for some +reason.

diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-by-step.foot b/deal.II/doc/tutorial/chapter-2.step-by-step/step-by-step.foot index 6e5ffd8ead..752a473868 100644 --- a/deal.II/doc/tutorial/chapter-2.step-by-step/step-by-step.foot +++ b/deal.II/doc/tutorial/chapter-2.step-by-step/step-by-step.foot @@ -3,7 +3,7 @@ diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/toc.html b/deal.II/doc/tutorial/chapter-2.step-by-step/toc.html index 35973eff1c..39226aa640 100644 --- a/deal.II/doc/tutorial/chapter-2.step-by-step/toc.html +++ b/deal.II/doc/tutorial/chapter-2.step-by-step/toc.html @@ -86,7 +86,8 @@ At present, the following programs exist:
Step 6
What's new: Adaptive local - refinement. Handling of hanging nodes. + refinement. Handling of hanging nodes. Catching of exceptions in + the ``main'' function.
-- 2.39.5