Paper Info
Title
Averaging Techniques for the A Posteriori BEM Error Control for a Hypersingular Integral Equation in Two Dimensions
Abstract
Averaging techniques or gradient recovery techniques are frequently employed tools for the a posteriori finite element error analysis. Their very recent mathematical justification for partial differential equations allows unstructured meshes and nonsmooth exact solutions. This paper establishes an averaging technique for the hypersingular integral equation on a one-dimensional boundary and presents numerical examples that show averaging techniques can be employed for an effective mesh-refining algorithm. For the discussed test examples, the provided estimator estimates the (in general unknown) error very accurately in the sense that the quotient error/estimator stays bounded with a value close to $1$.
Year
DOI
Venue
2007
10.1137/050623930
SIAM J. Scientific Computing
Keywords
Field
DocType
a posteriori bem error,galerkin method,effective mesh-refining algorithm,averaging techniques,hypersingular integral equation,a posteriori error estimate,quotient error,adaptive algorithm,posteriori finite element error,general unknown,gradient recovery technique,averaging technique,nonsmooth exact solution,zz error estimator,one-dimensional boundary,bound- ary element method,numerical example,finite element,boundary element method,integral equation,two dimensions,error control,partial differential equation,exact solution
Differential equation,Mathematical optimization,Mathematical analysis,Method of averaging,Integral equation,Finite element method,Boundary element method,Numerical analysis,Partial differential equation,Mathematics,Estimator
Journal
Volume
Issue
ISSN
29
2
1064-8275
Citations 
PageRank 
References 
4
0.48
4
Authors
2
Name
Order
Citations
PageRank
C Carstensen1944163.02
Dirk Praetorius212122.50