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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

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.

Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

References

  1. P. Ciarlet, Introduction to Numerical Linear Algebra and Optimization, Cambridge Texts in Applied Mathematics, 40 West 20th street, New York, NY, 1998.
  2. F. Gibou, R. Fedkiw, L.-T. Cheng and M. Kang, A second order accurate symmetric discretization of the Poisson equation on irregular domains, J. Comput. Phys., 176 (2002), 205-227. https://doi.org/10.1006/jcph.2001.6977
  3. Y.-T. Ng, C. Min and F. Gibou, An efficient fluid-solid coupling algorithm for single-phase flows, J. Comput. Phys., 228 (2009), 8807-8829. https://doi.org/10.1016/j.jcp.2009.08.032
  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
  5. J. W. Purvis and J. E. Burhalter, Prediction of critical Mach number for store configurations, AIAA J., 17 (1979), 1170-1177. https://doi.org/10.2514/3.7617
  6. J. C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, SIAM, Philadelphia, PA, 2004.