Stencils with isotropic discretization error for differential operators

M. Patra; M.E.J. Karttunen

doi:10.1002/num.20129

Stencils with isotropic discretization error for differential operators

M. Patra, M.E.J. Karttunen

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

57 Citaten (Scopus)

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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

Originele taal-2	Engels
Pagina's (van-tot)	936-953
Tijdschrift	Numerical Methods for Partial Differential Equations
Volume	22
Nummer van het tijdschrift	4
DOI's	https://doi.org/10.1002/num.20129
Status	Gepubliceerd - 2006

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10.1002/num.20129

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title = "Stencils with isotropic discretization error for differential operators",

abstract = "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",

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AB - 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

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Stencils with isotropic discretization error for differential operators

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