Asymptotic expansions of the error of spline Galerkin boundary element methods |
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Authors: | Michel Crouzeix Francisco-Javier Sayas |
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Institution: | (1) I.R.M.A.R., Université de Rennes 1, Campus de Beaulieu, F-35042 Rennes Cedex, France , FR;(2) Departamento de Matemática Aplicada, Edificio de Matemáticas, Campus Universitario, E-50009 Zaragoza, Spain , ES |
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Abstract: | Summary. In this paper we analyse the existence of asymptotic expansions of the error of Galerkin methods with splines of arbitrary
degree for the approximate solution of integral equations with logarithmic kernels. These expansions are obtained in terms
of an interpolation operator and are useful for the application of Richardson extrapolation and for obtaining sharper error
bounds. We also present and analyse a family of fully discrete spline Galerkin methods for the solution of the same equations.
Following the analysis of Galerkin methods, we show the existence of asymptotic expansions of the error.
Received May 18, 1995 / Revised version received April 11, 1996 |
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Keywords: | Mathematics Subject Classification (1991): |
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