Interior maximum norm estimates for finite element methods

Schatz, A. H.; Wahlbin, L. B.

doi:10.1090/S0025-5718-1977-0431753-X

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 ${\Omega _1}$ 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 ${\Omega _1}$ .

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