Mesh-Centered Finite Differences from Nodal Finite Elements for Elliptic Problems

J. P. Hennart, E. Del Valle

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Abstract

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. © 1998 John Wiley & Sons, Inc.
Original languageAmerican English
Pages (from-to)439-465
Number of pages392
JournalNumerical Methods for Partial Differential Equations
DOIs
StatePublished - 1 Jan 1998

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