]> https://gitweb.dealii.org/ - dealii-svn.git/commitdiff
Abstract of SIAM J. Sci. Comp. of Hartmann and Houston.
authorhartmann <hartmann@0785d39b-7218-0410-832d-ea1e28bc413d>
Fri, 4 May 2001 12:21:23 +0000 (12:21 +0000)
committerhartmann <hartmann@0785d39b-7218-0410-832d-ea1e28bc413d>
Fri, 4 May 2001 12:21:23 +0000 (12:21 +0000)
git-svn-id: https://svn.dealii.org/trunk@4536 0785d39b-7218-0410-832d-ea1e28bc413d

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+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"
+   "http://www.w3.org/TR/REC-html40/strict.dtd">
+<html>
+  <head>
+    <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
+    <link href="../../print.css" rel="StyleSheet" title="deal.II Homepage" media="print">
+    <title>The deal.II Homepage</title>
+    <meta name="author" content="Ralf Hartmann <Ralf Hartmann@iwr.uni-heidelberg.de>">
+    <meta name="keywords" content="Publications on and with deal.II"></head>
+  <body>
+
+
+<H3>Abstract:</H3>
+<DIR>
+We consider the <em>a posteriori</em> 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
+<em>a posteriori</em> 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 <em>a posteriori</em>
+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
+<em>ad hoc</em> error indicators. 
+
+</DIR>
+<P>
+<BR><HR>
+<ADDRESS>
+<I>Ralf Hartmann</I>
+<BR><I>2000-05-04</I>
+</ADDRESS>
+</BODY>
+</HTML>

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