Higher order local accuracy by averaging in the finite element method
Authors:
J. H. Bramble and A. H. Schatz
Journal:
Math. Comp. 31 (1977), 94111
MSC:
Primary 65N30
MathSciNet review:
0431744
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Abstract: Let be a RitzGalerkin 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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 J. H. BRAMBLE & S. HILBERT, "Bounds for a class of linear functionals with applications to Hermite interpolation," Numer. Math., v. 16, 1971, pp. 362369. MR 0290524 (44:7704)
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 J. H. BRAMBLE, J. A. NITSCHE & A. H. SCHATZ, "Maximumnorm interior estimates for RitzGalerkin methods," Math. Comp., v. 29, 1975, pp. 677688. MR 0398120 (53:1975)
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 J. H. BRAMBLE & A. H. SCHATZ, "Estimates for spline projection," Rev. Française Automat. Informat. Recherche Opérationnelle Analyse Numérique, v. 10, no 8, août 1976, pp. 537. MR 0436620 (55:9563)
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 J. H. BRAMBLE & A. H. SCHATZ, "Higher order local accuracy by averaging in the finite element method," Mathematical Aspects of Finite Elements in Partial Differential Equations (Proc. Sympos., Math. Res. Center, Univ. of Wisconsin, Madison, 1974), edited by Carl de Boor, Academic Press, New York, 1974, pp. 114. MR 50 #1525. MR 0657964 (58:31903)
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DOI:
http://dx.doi.org/10.1090/S00255718197704317449
PII:
S 00255718(1977)04317449
Article copyright:
© Copyright 1977
American Mathematical Society
