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Stencils with isotropic discretization error for differential operators
Author(s) -
Patra Michael,
Karttunen Mikko
Publication year - 2006
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20129
Subject(s) - mathematics , isotropy , discretization , discretization error , differential operator , differential (mechanical device) , mathematical analysis , physics , thermodynamics , quantum mechanics
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 ( h 2 ) results are given while for two dimensions both ( h 2 ) and ( h 4 ) 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%. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006
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