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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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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Additional Information
DOI:
https://doi.org/10.1090/S0025-5718-1977-0431744-9
Article copyright:
© Copyright 1977
American Mathematical Society