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Mathematics of Computation

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Interior estimates for Ritz-Galerkin methods

Authors: Joachim A. Nitsche and Alfred H. Schatz
Journal: Math. Comp. 28 (1974), 937-958
MSC: Primary 65N30; Secondary 35JXX
MathSciNet review: 0373325
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Abstract: Interior a priori error estimates in Sobolev norms 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 both uniform and nonuniform meshes. It is shown that the error in an interior domain $ \Omega $ 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 $. Additional results are given in the case when the subspaces are defined on a uniform mesh. Applications to specific boundary value problems are given.

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Article copyright: © Copyright 1974 American Mathematical Society