The spline collocation method for parabolic boundary integral equations on smooth curves |
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| Authors: | M Costabel J Saranen |
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| Institution: | (1) Département de Mathématiques, Université de Rennes I, Campus de Beaulieu, 35042 Rennes Cedex, France (e-mail: Martin.Costabel@univ-rennes1.fr) , FR;(2) Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, FIN-90014, Finland (e-mail: jukka.saranen@oulu.fi) , FI |
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| Abstract: | Summary. We consider the spline collocation method for a class of parabolic pseudodifferential operators. We show optimal order convergence
results in a large scale of anisotropic Sobolev spaces. The results cover the classical boundary integral equations for the
heat equation in the general case where the spatial domain has a smooth boundary in the plane. Our proof is based on a localization
technique for which we use our recent results proved for parabolic pseudodifferential operators. For the localization we need
also some special spline approximation results in anisotropic Sobolev spaces.
Received May 17, 2001 / Revised version received February 19, 2002 / Published online April 17, 2002 |
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| Keywords: | Mathematics Subject Classification (1991): 65R20 45L10 CR G 1 9 |
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