Interior maximum norm estimates for finite element methods

Authors:
A. H. Schatz and L. B. Wahlbin

Journal:
Math. Comp. **31** (1977), 414-442

MSC:
Primary 65N30

DOI:
https://doi.org/10.1090/S0025-5718-1977-0431753-X

MathSciNet review:
0431753

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Abstract: Interior a priori error estimates in the maximum norm are derived from interior Ritz-Galerkin equations which are common to a class of methods used in approximating solutions of second order elliptic boundary value problems. The estimates are valid for a large class of piecewise polynomial subspaces used in practice, which are defined on quasi-uniform meshes.

It is shown that the error in an interior domain can be estimated with the best order of accuracy that is possible locally for the subspaces used plus the error in a weaker norm over a slightly larger domain which measures the effects from outside of the domain .

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DOI:
https://doi.org/10.1090/S0025-5718-1977-0431753-X

Article copyright:
© Copyright 1977
American Mathematical Society