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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2003; 40(6): 1075-1083

Printed November 1, 2003

Copyright © The Korean Mathematical Society.

Curved domain approximation in Dirichlet's problem

Miyoung Lee, Sang Mok Choo, and Sang Kwon Chung

Abstract

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The purpose of this paper is to investigate the piecewise polynomial approximation for the curved boundary. We analyze the error of an approximated solution due to this approximation and then compare the approximation errors for the cases of polygonal and piecewise polynomial approximations for the curved boundary. Based on the results of analysis, $p$-version numerical methods for solving Dirichlet's problems are applied to any smooth curved domain.

Keywords: curved domain, polynomial boundary approximation, p-version, Poisson equation

MSC numbers: Primary 65M06, 65M12, 65M15

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