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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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Multigrid analysis for the time dependent Stokes problem
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by Maxim A. Olshanskii PDF
Math. Comp. 81 (2012), 57-79 Request permission

Abstract:

Certain implicit time stepping procedures for the incompressible Stokes or Navier-Stokes equations lead to a singular-perturbed Stokes type problem at each time step. The paper presents a convergence analysis of a geometric multigrid solver for the system of linear algebraic equations resulting from the disretization of the problem using a finite element method. Several smoothing iterative methods are considered: a smoother based on distributive iterations, the Braess-Sarazin and inexact Uzawa smoother. Convergence analysis is based on smoothing and approximation properties in special norms. A robust (independent of time step and mesh parameter) estimate is proved for the two-grid and multigrid W-cycle convergence factors.
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Additional Information
  • Maxim A. Olshanskii
  • Affiliation: Department of Mechanics and Mathematics, M. V. Lomonosov Moscow State University, Moscow 119899, Russia
  • MR Author ID: 343398
  • Email: Maxim.Olshanskii@mtu-net.ru
  • Received by editor(s): April 29, 2009
  • Received by editor(s) in revised form: October 20, 2010
  • Published electronically: May 23, 2011
  • Additional Notes: The author was partially supported through the RFBR Grant 11-01-00767 and 09-01-00115
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 81 (2012), 57-79
  • MSC (2010): Primary 65N55, 65N30, 65N15, 65F10
  • DOI: https://doi.org/10.1090/S0025-5718-2011-02494-4
  • MathSciNet review: 2833487