Discrete boundary element methods on general meshes in 3D
type: Item
instance of: scholarly article
title: Discrete boundary element methods on general meshes in 3D
zbMATH Open document ID: 0966.65090
published in: Numerische Mathematik
publication date: 2001-08-02T00:00:00Z
review text: The authors study stability and convergence of fully discrete Galerkin methods for boundary integral equations on bounded piecewise smooth surfaces in \(\mathbb R^3.\) The integral operators have to be strongly elliptic, but the meshes are not assumed to be quasiuniform. The methods are treated by generalisations of standard inverse estimates to the non-quasiuniform case. The authors analyse the integration errors for nearly singular and smooth Galerkin integrals in order to determine the accuracy of quadrature rules ensuring that the resulting discrete Galerkin method enjoys the same stability and convergence properties as the true Galerkin method. The theory, which covers quite general surfaces and meshes, is applied to linear boundary elements on triangles and corresponding quadrature rules. As an example the required accuracy of quadrature rules for the standard integral operators from Laplace's equation is given which preserve the stability and convergence properties of Galerkin's method in the energy norm.
reviewed by: Gunther Schmidt
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 1491754
zbMATH Keywords: boundary integral equations
zbMATH Keywords: discrete Galerkin method
zbMATH Keywords: quadrature of Galerkin integrals
zbMATH Keywords: boundary element methods
zbMATH Keywords: stability
zbMATH Keywords: convergence
zbMATH Keywords: Laplace's equation
author: I. G. Graham
author: Wolfgang Hackbusch
author: S. Sauter
MaRDI profile type: Publication
DOI: 10.1007/S002110000162
description: scientific article; zbMATH DE number 1491754