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Mesh-centered finite differences from nodal finite elements for elliptic problems

✍ Scribed by J. P. Hennart; E. del Valle

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 472 KB
Volume: 14
Category: Article
ISSN: 0749-159X
DOI: 10.1002/(sici)1098-2426(199807)14:4<439::aid-num2>3.0.co;2-l

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✦ Synopsis

After it is shown that the classical five-point mesh-centered finite difference scheme can be derived from a low-order nodal finite element scheme by using nonstandard quadrature formulae, higher-order block mesh-centered finite difference schemes for second-order elliptic problems are derived from higher-order nodal finite elements with nonstandard quadrature formulae as before, combined to a procedure known as "transverse integration." Numerical experiments with uniform and nonuniform meshes and different types of boundary conditions confirm the theoretical predictions, in discrete as well as continuous norms.

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