Two-level methods for the single layer potential in \(\mathbb{R}^3\)
type: Item
instance of: scholarly article
title: Two-level methods for the single layer potential in \(\mathbb{R}^3\)
zbMATH Open document ID: 0901.65072
DOI: 10.1007/BF02684335
author: Patrick Mund
author: J. Weiße
author: Ernst P. Stephan
published in: Computing
publication date: 1998-11-11T00:00:00Z
review text: The rough contents of this very elaborate paper are as follows: 0. Introduction, 1. Notations and preliminaries, 2. Spectral analysis for two level additive Schwarz operator, 3. A posteriori error estimate, 4. Adaptive refinement algorithm , 5. Numerical results and references. The authors consider weakly singular integral equations of the first kind on open surface pieces. They obtain approximate solutions using the \(h\)-version of the Galerkin boundary element method. Moreover they introduce two-level additive Schwarz operators for non-overlaping domain decompositions and estimate the condition numbers of these operators with respect to the meshsize. By use of the above operators they obtain an a posteriori error estimate. The theoretical results are illustrated by some numerical examples.
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65N15
zbMATH DE Number: 1160314
zbMATH Keywords: weakly singular integral equations
zbMATH Keywords: \(h\)-version
zbMATH Keywords: Galerkin boundary element method
zbMATH Keywords: two-level additive Schwarz operators
zbMATH Keywords: domain decomposition
zbMATH Keywords: hierarchical basis
zbMATH Keywords: a posteriori error estimate
zbMATH Keywords: adaptive algorithm
zbMATH Keywords: numerical examples
zbMATH Keywords: condition numbers
reviewed by: Calin Ioan Gheorghiu
MaRDI profile type: Publication
cites work: Q4112938
cites work: Adaptive multivlevel methods in three space dimensions
cites work: Stable multiscale bases and local error estimation for elliptic problems
cites work: Concepts of an adaptive hierarchical finite element code
cites work: Q3470840
cites work: Exponential convergence of the \(hp\)-version for the boundary element method on open surfaces
cites work: Q4356903
cites work: Q3995346
cites work: Boundary integral equations for screen problems in \({\mathbb{R}}^ 3\)
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description: scientific article; zbMATH DE number 1160314