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
Original language | English |
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Pages (from-to) | 936-953 |
Journal | Numerical Methods for Partial Differential Equations |
Volume | 22 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2006 |