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Article Dans Une Revue BIT Numerical Mathematics Année : 2019

Compact finite difference schemes of arbitrary order for the Poisson equation in arbitrary dimensions

Erwan Deriaz

Résumé

A formulation of the Taylor expansion with symmetric polynomial algebra allows to compute the coefficients of compact finite difference schemes, which solve the Poisson equation at an arbitrary order of accuracy on a uniform Cartesian grid in arbitrary dimensions. This construction produces original high order schemes which respect the Discrete Maximum Principle: a tenth order scheme in dimension three and several sixth order schemes in arbitrary dimension. Numerical experiments validate the accuracy of these schemes.
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hal-01998201 , version 1 (29-01-2019)

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Erwan Deriaz. Compact finite difference schemes of arbitrary order for the Poisson equation in arbitrary dimensions. BIT Numerical Mathematics, 2019, ⟨10.1007/s10543-019-00772-5⟩. ⟨hal-01998201⟩

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