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http://dx.doi.org/10.12941/jksiam.2014.18.051

A REVIEW OF THE SUPRA-CONVERGENCES OF SHORTLEY-WELLER METHOD FOR POISSON EQUATION  

Yoon, Gangjoon (INSTITUTE OF MATHEMATICAL SCIENCES, EWHA WOMANS UNIVERSITY)
Min, Chohong (DEPARTMENT OF MATHEMATICS, EWHA WOMANS UNIVERSITY)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.18, no.1, 2014 , pp. 51-60 More about this Journal
Abstract
The Shortley-Weller method is a basic finite difference method for solving the Poisson equation with Dirichlet boundary condition. In this article, we review the analysis for supra-convergence of the Shortley-Weller method. Though consistency error is first order accurate at some locations, the convergence order is globally second order. We call this increase of the order of accuracy, supra-convergence. Our review is not a simple copy but serves a basic foundation to go toward yet undiscovered analysis for another supra-convergence: we present a partial result for supra-convergence for the gradient of solution.
Keywords
Shortley-Weller; finite difference method; Poisson equattion; supra-convergence;
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