Fully discrete Galerkin methods for systems of boundary integral equations
type: Item
instance of: scholarly article
title: Fully discrete Galerkin methods for systems of boundary integral equations
zbMATH Open document ID: 0882.65107
DOI: 10.1016/S0377-0427(97)00069-1
author: Francisco-Javier Sayas
published in: Journal of Computational and Applied Mathematics
publication date: 1998-03-05T00:00:00Z
review text: The author considers a class of systems of boundary integral equations of the first kind, coupled with some side conditions of integral type and including some additional scalar unknowns, in order to guarantee the existence and uniqueness of the solution. The stability and convergence of a spline Galerkin method is then considered. He also proves the existence of a kind of asymptotic expansion of the error in the powers of the discretized parameter. The core of the paper is a generalization of the classical Galerkin collocation method in the sense that the method uses splines of arbitrary degree and a wider choice of quadrature formulae. An asymptotic expansion of the consistency error for this method is also carried out. The author ends the paper with a postprocessing which includes the computation of the solution of the boundary value problem associated to the boundary integral equation.
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N15
zbMATH DE Number: 1043290
zbMATH Keywords: fully discrete Galerkin methods
zbMATH Keywords: extrapolation
zbMATH Keywords: error bounds
zbMATH Keywords: systems of boundary integral equations
zbMATH Keywords: stability
zbMATH Keywords: convergence
zbMATH Keywords: spline Galerkin method
zbMATH Keywords: Galerkin collocation method
zbMATH Keywords: quadrature formulae
reviewed by: Calin Ioan Gheorghiu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1043290