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Mathematics of Computation

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Maximum-norm interior estimates for Ritz-Galerkin methods

Authors: James H. Bramble, Joachim A. Nitsche and Alfred H. Schatz
Journal: Math. Comp. 29 (1975), 677-688
MSC: Primary 65N15
MathSciNet review: 0398120
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Abstract: In this paper we obtain, by simple means, interior maximum-norm estimates for a class of Ritz-Galerkin methods used for approximating solutions of second order elliptic boundary value problems in ${{\mathbf {R}}^N}$. The estimates are proved when the approximating subspaces are any of a large class of piecewise polynomial subspaces which we assume here to be defined on a uniform mesh on the interior domain. Optimal rates of convergence are obtained.

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Article copyright: © Copyright 1975 American Mathematical Society