Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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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)
  • Received : 2013.11.07
  • Accepted : 2014.02.21
  • Published : 2014.03.25
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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.

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References

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