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Stencils with isotropic discretization error for differential operators
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| NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS |
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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 O(h(2)) results are given while for two dimensions both O(h(2)) and O(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%.
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difference schemes, Laplacian, isotropic discretization
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