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Curved Domain Approximation in Dirichlet's Problem
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Abstract
The purpose of this paper is to investigate thepiecewise polynomial approximation for the curved boundary. Weanalyze the error of an approximated solution due to thisapproximation and then compare the approximation errors for thecases of polygonal and piecewise polynomial approximations for thecurved boundary. Based on the results of analysis, p-versionnumerical methods for solving Dirichlet's problems are applied toany smooth curved domain.
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