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Applicable Analysis
An International Journal
Volume 86, 2007 - Issue 2
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Original Articles

Interior maximum norm estimates for finite element discretizations of the Stokes equations

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Pages 251-260 | Received 30 Nov 2006, Accepted 01 Dec 2006, Published online: 22 Feb 2007
 

Abstract

Interior estimates are proved in the L norm for stable finite element discretizations of the Stokes equations on translation invariant meshes. These estimates yield information about the quality of the finite element solution in subdomains a positive distance from the boundary. While they have been established for second-order elliptic problems, these interior, or local, maximum norm estimates for the Stokes equations are new. By applying finite differenciation methods on a translation invariant mesh, we obtain optimal convergence rates in the mesh size h in the maximum norm. These results can be used for analyzing superconvergence in finite element methods for the Stokes equations.

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