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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


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


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.
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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:
  • 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:
  • MathSciNet review: 2833486