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Journal of Scientific Computing

, Volume 74, Issue 2, pp 631–639 | Cite as

Convergence Analysis in the Maximum Norm of the Numerical Gradient of the Shortley–Weller Method

  • Jiwon Seo
  • Seung-yeal Ha
  • Chohong Min
Article

Abstract

The Shortley–Weller method is a standard central finite-difference-method for solving the Poisson equation in irregular domains with Dirichlet boundary conditions. It is well known that the Shortley–Weller method produces second-order accurate solutions and it has been numerically observed that the solution gradients are also second-order accurate; a property known as super-convergence. The super-convergence was proved in the \(L^{2}\) norm in Yoon and Min (J Sci Comput 67(2):602–617, 2016). In this article, we present a proof for the super-convergence in the \(L^{\infty }\) norm.

Keywords

Shortley–Weller Finite difference method Super-convergence Convergence analysis 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Ewha Womans UniversitySeoulRepublic of Korea
  2. 2.Seoul National UniversitySeoulRepublic of Korea

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