From 88e337abc81c9ff3226b83334f50bb08c01fded0 Mon Sep 17 00:00:00 2001 From: Ralf Hartmann Date: Fri, 4 May 2001 12:21:23 +0000 Subject: [PATCH] Abstract of SIAM J. Sci. Comp. of Hartmann and Houston. git-svn-id: https://svn.dealii.org/trunk@4536 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/doc/publications/2001/hh-1.html | 43 +++++++++++++++++++++++++ 1 file changed, 43 insertions(+) create mode 100644 deal.II/doc/publications/2001/hh-1.html diff --git a/deal.II/doc/publications/2001/hh-1.html b/deal.II/doc/publications/2001/hh-1.html new file mode 100644 index 0000000000..4f499cf455 --- /dev/null +++ b/deal.II/doc/publications/2001/hh-1.html @@ -0,0 +1,43 @@ + + + + + + The deal.II Homepage + + + + + +

Abstract:

+ +We consider the a posteriori error analysis +and adaptive mesh design for discontinuous Galerkin finite +element approximations to systems of nonlinear +hyperbolic conservation laws. +In particular, we discuss the question of error estimation for general +linear and nonlinear functionals of the solution; typical examples +include the +outflow flux, local average and pointwise value, as well as the lift +and drag coefficients of a body immersed in an inviscid fluid. +By employing a duality argument, we derive so-called weighted or Type I +a posteriori error bounds; in these error estimates +the element--residuals are multiplied by local weights involving +the solution of a certain dual problem. Based on these a posteriori +bounds, we design and implement the corresponding adaptive algorithm +to ensure efficient and reliable control of the error in the +computed functional. The theoretical results are illustrated by a series of +numerical experiments. In particular, we demonstrate the superiority +of the proposed approach over standard mesh refinement algorithms which employ +ad hoc error indicators. + + +

+


+
+Ralf Hartmann +
2000-05-04 +
+ + -- 2.39.5