Higher order local accuracy by averaging in the finite element method

Bramble, J. H.; Schatz, A. H.

doi:10.1090/S0025-5718-1977-0431744-9

Higher order local accuracy by averaging in the finite element method
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by J. H. Bramble and A. H. Schatz PDF

Math. Comp. 31 (1977), 94-111 Request permission

Abstract:

Let ${u_h}$ 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 ${u_h}$ in the neighborhood of a point x we may (for a wide class of problems) construct an approximation to $u(x)$ which is often a better approximation than ${u_h}(x)$ itself. The "averaging" operator does not depend on the specific elliptic operator involved and is easily constructed.

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Quart. Appl. Math.

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