Higher order local accuracy by averaging in the finite element method

Authors:
J. H. Bramble and A. H. Schatz

Journal:
Math. Comp. **31** (1977), 94-111

MSC:
Primary 65N30

DOI:
https://doi.org/10.1090/S0025-5718-1977-0431744-9

MathSciNet review:
0431744

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Abstract: Let be a Ritz-Galerkin approximation, corresponding to the solution *u* of an elliptic boundary value problem, which is based on a uniform subdivision in the interior of the domain. In this paper we show that by "averaging" the values of in the neighborhood of a point *x* we may (for a wide class of problems) construct an approximation to which is often a better approximation than itself. The "averaging" operator does not depend on the specific elliptic operator involved and is easily constructed.

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DOI:
https://doi.org/10.1090/S0025-5718-1977-0431744-9

Article copyright:
© Copyright 1977
American Mathematical Society