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Solving Laplace problems with corner singularities via rational functions

Abstract:

A new method is introduced for solving Laplace problems on 2D regions with corners by approximation of boundary data by the real part of a rational function with fixed poles exponentially clustered near each corner. Greatly extending a result of D. J. Newman in 1964 in approximation theory, we first prove that such approximations can achieve root-exponential convergence for a wide range of problems, all the way up to the corner singularities. We then develop a numerical method to compute appr...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1137/19M125947X

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Balliol College
Role:
Author
ORCID:
0000-0003-2504-1709
Publisher:
Society for Industrial and Applied Mathematics Publisher's website
Journal:
SIAM Journal on Numerical Analysis Journal website
Volume:
57
Issue:
5
Pages:
2074-2094
Publication date:
2019-09-05
Acceptance date:
2019-06-20
DOI:
Source identifiers:
998869
Keywords:
Pubs id:
pubs:998869
UUID:
uuid:366e6e2b-a6c9-42e1-b2bd-1d77c1dc2a6e
Local pid:
pubs:998869
Deposit date:
2019-06-21

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