Quadrature for \(hp\)-Galerkin BEM in \(\mathbb{R}^3\)
type: Item
instance of: scholarly article
title: Quadrature for \(hp\)-Galerkin BEM in \(\mathbb{R}^3\)
zbMATH Open document ID: 0901.65069
author: S. Sauter
author: Christoph Schwab
published in: Numerische Mathematik
publication date: 1998-11-15T00:00:00Z
review text: The authors describe and analyze an \(hp\)-type method for the discretization of integral operators with Cauchy singular kernels on two-dimensional piecewise analytic manifolds with edges and corners. An exponential rate of convergence can be ensured under certain assumptions concerning the behavior of the kernel functions, the mesh grading and the polynomial order of the trial functions. The total numerical effort, however, grows algebraically with the number of degrees of freedom. To this end, special quadrature techniques are necessary which involve coordinate transformations, splitting of the integration domain and regularization techniques. These strategies are described in each detail. Several cases must be distinguished and handled separately. Furthermore, a priori estimates for the necessary number of quadrature sample points are given. All these things are not only of interest for the \(hp\)-Galerkin method. They are applicable for other versions of the boundary element method (BEM) as well.
reviewed by: Andreas Pomp
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 45E05
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 1145994
zbMATH Keywords: Gaussian quadrature
zbMATH Keywords: \(hp\)-Galerkin method
zbMATH Keywords: Cauchy singular kernels
zbMATH Keywords: convergence
zbMATH Keywords: boundary element method
MaRDI profile type: Publication
full work available at URL: s002110050311
OpenAlex ID: W2026894598
DOI: 10.1007/S002110050311
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description: scientific article; zbMATH DE number 1145994