Asymptotic analysis of the conventional and invariant schemes for the method of fundamental solutions applied to potential problems in doubly-connected regions

The aim of this paper is to develop mathematical theory of the conventional and invariant schemes for the method of fundamental solutions used to solve potential problems in doubly-connected regions. Particularly, we prove that an approximate solution actually exists uniquely under some conditions,...

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Bibliographic Details
Published in:Japan journal of industrial and applied mathematics 2017-04, Vol.34 (1), p.177-228
Main Author: Sakakibara, Koya
Format: Article
Language:English
Subjects:
Applications of Mathematics
Asymptotic methods
Computational Mathematics and Numerical Analysis
Invariants
Mathematics
Mathematics and Statistics
Original Paper
Sharpness
Sobolev space
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Summary:The aim of this paper is to develop mathematical theory of the conventional and invariant schemes for the method of fundamental solutions used to solve potential problems in doubly-connected regions. Particularly, we prove that an approximate solution actually exists uniquely under some conditions, and that the error decays exponentially when the boundary data are analytic, and algebraically when they are not analytic but belong to some Sobolev spaces. Moreover, we present results of several numerical experiments in order to show the sharpness of our error estimate.
ISSN:0916-7005
1868-937X
DOI:10.1007/s13160-017-0241-4