Superconvergence of Solution Derivatives of the Shortley-Weller Difference Approximation to Elliptic Equations with Singularities involving the Mixed Type of Boundary Conditions

Z-C. Li, Q. Fang, Song Wang, H-Y. Hu

    Research output: Contribution to journalArticle

    5 Citations (Scopus)

    Abstract

    This paper presents a superconvergence analysis for the Shortley-Weller finite difference approximation of second-order self-adjoint elliptic equations with unbounded derivatives on a polygonal domain with the mixed type of boundary conditions. In this analysis, we first formulate the method as a special finite element/volume method. We then analyze the convergence of the method in a finite element framework. An O(h(1.5))-order superconvergence of the solution derivatives in a discrete H-1 norm is obtained. Finally, numerical experiments art provided to support the theoretical convergence rate obtained.
    Original languageEnglish
    Pages (from-to)161-196
    JournalNumerical Functional Analysis and Optimization
    Volume29
    Issue number1-2
    DOIs
    Publication statusPublished - 2008

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