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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Analysis of an adaptive Uzawa finite element method for the nonlinear Stokes problem
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by Christian Kreuzer PDF
Math. Comp. 81 (2012), 21-55 Request permission

Abstract:

We design and study an adaptive algorithm for the numerical solution of the stationary nonlinear Stokes problem. The algorithm can be interpreted as a disturbed steepest descent method, which generalizes Uzawa’s method to the nonlinear case. The outer iteration for the pressure is a descent method with fixed step-size. The inner iteration for the velocity consists of an approximate solution of a nonlinear Laplace equation, which is realized with adaptive linear finite elements. The descent direction is motivated by the quasi-norm which naturally arises as distance between velocities. We establish the convergence of the algorithm within the framework of descent direction methods.
References
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Additional Information
  • Christian Kreuzer
  • Affiliation: Fakultät für Mathematik, Universität Duisburg-Essen, Forsthausweg 2, Duisburg, Germany 47057
  • MR Author ID: 833122
  • ORCID: 0000-0003-2923-4428
  • Email: christian.kreuzer@uni-due.de
  • Received by editor(s): December 16, 2009
  • Received by editor(s) in revised form: January 22, 2011
  • Published electronically: May 11, 2011
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 81 (2012), 21-55
  • MSC (2010): Primary 65N30, 65N12, 35J60
  • DOI: https://doi.org/10.1090/S0025-5718-2011-02524-X
  • MathSciNet review: 2833486