Journal of the Korean Society for Industrial and Applied Mathematics

  • 제18권1호
  • /
  • Pages.51-60
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  • 2014
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  • 1226-9433(pISSN)
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  • 1229-0645(eISSN)
한국산업응용수학회 (Korean Society for Industrial and Applied Mathematics)
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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)
  • 투고 : 2013.11.07
  • 심사 : 2014.02.21
  • 발행 : 2014.03.25
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초록

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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참고문헌

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  4. Y.-T. Ng, H. Chen, C. Min and F. Gibou, Guidelines for Poisson solvers on irregular domains with Dirichlet boundary conditions using the ghost fluid method, J. Sci. Comput., 41 (2009), 300-320. https://doi.org/10.1007/s10915-009-9299-8
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피인용 문헌

  1. Super-Convergence in Maximum Norm of the Gradient for the Shortley-Weller Method vol.75, pp.2, 2014, https://doi.org/10.1007/s10915-017-0548-y
  2. A Second-Order Boundary Condition Capturing Method for Solving the Elliptic Interface Problems on Irregular Domains vol.81, pp.1, 2014, https://doi.org/10.1007/s10915-019-01016-y
  3. Higher order difference numerical analyses of a 2D Poisson equation by the interpolation finite difference method and calculation error evaluation vol.10, pp.12, 2014, https://doi.org/10.1063/5.0018915