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Mathematics of Computation

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Error estimators for nonconforming finite element approximations of the Stokes problem

Authors: Enzo Dari, Ricardo Durán and Claudio Padra
Journal: Math. Comp. 64 (1995), 1017-1033
MSC: Primary 65N30; Secondary 65N50, 76D07, 76M10
MathSciNet review: 1284666
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Abstract: In this paper we define and analyze a posteriori error estimators for nonconforming approximations of the Stokes equations. We prove that these estimators are equivalent to an appropriate norm of the error. For the case of piecewise linear elements we define two estimators. Both of them are easy to compute, but the second is simpler because it can be computed using only the right-hand side and the approximate velocity. We show how the first estimator can be generalized to higher-order elements. Finally, we present several numerical examples in which one of our estimators is used for adaptive refinement.

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Article copyright: © Copyright 1995 American Mathematical Society