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Mathematics of Computation

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Grad-div stablilization for Stokes equations

Authors: Maxim A. Olshanskii and Arnold Reusken
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Journal: Math. Comp. 73 (2004), 1699-1718
MSC (2000): Primary 65N30, 65N22, 76D07
Published electronically: December 19, 2003
MathSciNet review: 2059732
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Abstract: In this paper a stabilizing augmented Lagrangian technique for the Stokes equations is studied. The method is consistent and hence does not change the continuous solution. We show that this stabilization improves the well-posedness of the continuous problem for small values of the viscosity coefficient. We analyze the influence of this stabilization on the accuracy of the finite element solution and on the convergence properties of the inexact Uzawa method.

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Additional Information

Maxim A. Olshanskii
Affiliation: Dept. Mechanics and Mathematics, Moscow State University, Moscow 119899, Russia

Arnold Reusken
Affiliation: Institut für Geometrie und Praktische Mathematik, RWTH-Aachen, D-52056 Aachen, Germany

Keywords: Stokes equations, finite elements, augmented Lagrangian, inexact Uzawa
Received by editor(s): November 7, 2001
Received by editor(s) in revised form: March 5, 2003
Published electronically: December 19, 2003
Article copyright: © Copyright 2003 American Mathematical Society