Superconvergence of solution derivatives for the Shortley-Weller difference approximation for parabolic problems

Z-C. Li, Q. Fang, Song Wang

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    In [8-118, 9, 10, 11] a superconvergence analysis is derived for the smooth and singular Poisson equations by the finite difference method (FDM) using the Shortley-Weller approximation. In this article, we explore the superconvergence analysis for a parabolic equation using the Shortley-Weller approximation and the Crank-Nicolson scheme (CNS) in space and time discretization, respectively, denoted simply as FDM-CNS. The results of derivative superconvergence in [8-118, 9, 10, 11] can be extended to parabolic problems of smooth and singular solutions. The main results are as follows: when [image omitted] and [image omitted], the superconvergence rate O(h2 + k2) is derived for the solution derivatives in discrete H1 norms by the FDM-CNS on rectangular domains, where k is the time mesh spacing in the Crank-Nicolson scheme and h is the maximal mesh length of difference grids used. Note that the difference grids are not confined to be quasi-uniform, and local refinements are allowed for the solutions with unbounded derivatives. Numerical experiments are provided to support the superconvergence O(h2 + k2). [ABSTRACT FROM AUTHOR] Copyright of Numerical Functional Analysis & Optimization is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
    Original languageEnglish
    Pages (from-to)1360-1380
    JournalNumerical Functional Analysis and Optimization
    Volume30
    Issue number11/12
    DOIs
    Publication statusPublished - 2009

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