Error analysis of the Bergman kernel method with singular basis functions

Let G be a bounded Jordan domain in the complex plane with piecewise analytic boundary. We present theoretical estimates and numerical evidence for certain phenomena, regarding the application of the Bergman kernel method with algebraic and pole singular basis functions, for approximating the confor...

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Bibliographic Details
Published in:arXiv.org 2011-01
Main Authors: Lytrides, M, Stylianopoulos, N
Format: Article
Language:English
Subjects:
Basis functions
Conformal mapping
Error analysis
Kernels
Online Access:Get full text
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Summary:Let G be a bounded Jordan domain in the complex plane with piecewise analytic boundary. We present theoretical estimates and numerical evidence for certain phenomena, regarding the application of the Bergman kernel method with algebraic and pole singular basis functions, for approximating the conformal mapping of G onto the normalized disk. In this way, we complete the task of providing full theoretical justification of this method.
ISSN:2331-8422