Stencils with isotropic discretization error for differential operators

M. Patra, M.E.J. Karttunen

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    58 Citations (Scopus)


    We derive stencils, i.e., difference schemes, for differential operators for which the discretization error becomes isotropic in the lowest order. We treat the Laplacian, Bilaplacian (= biharmonic operator), and the gradient of the Laplacian both in two and three dimensions. For three dimensions [MATHEMATICAL SCRIPT CAPITAL O](h2) results are given while for two dimensions both [MATHEMATICAL SCRIPT CAPITAL O](h2) and [MATHEMATICAL SCRIPT CAPITAL O](h4) results are presented. The results are also available in electronic form as a Mathematica file. It is shown that the extra computational cost of an isotropic stencil usually is less than 20%. Keywords: difference schemes;Laplacian;isotropic discretization
    Original languageEnglish
    Pages (from-to)936-953
    JournalNumerical Methods for Partial Differential Equations
    Issue number4
    Publication statusPublished - 2006


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