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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.

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Analysis of a sequential regularization method for the unsteady Navier-Stokes equations
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by Xiliang Lu, Ping Lin and Jian-Guo Liu PDF
Math. Comp. 77 (2008), 1467-1494 Request permission

Abstract:

The incompressibility constraint makes Navier-Stokes equations difficult. A reformulation to a better posed problem is needed before solving it numerically. The sequential regularization method (SRM) is a reformulation which combines the penalty method with a stabilization method in the context of constrained dynamical systems and has the benefit of both methods. In the paper, we study the existence and uniqueness for the solution of the SRM and provide a simple proof of the convergence of the solution of the SRM to the solution of the Navier-Stokes equations. We also give error estimates for the time discretized SRM formulation.
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Additional Information
  • Xiliang Lu
  • Affiliation: Department of Mathematics, National University of Singapore, Science Drive 2, Singapore 117543, Singapore
  • Address at time of publication: Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenberger Strasse 69, A-4040 Linz, Austria
  • Email: lu_xiliang@hotmail.com
  • Ping Lin
  • Affiliation: Department of Mathematics, National University of Singapore, Science Drive 2, Singapore 117543, Singapore
  • Email: matlinp@nus.edu.sg
  • Jian-Guo Liu
  • Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742-4015
  • MR Author ID: 233036
  • ORCID: 0000-0002-9911-4045
  • Email: jliu@math.umd.edu
  • Received by editor(s): July 25, 2006
  • Received by editor(s) in revised form: June 4, 2007
  • Published electronically: February 1, 2008
  • Additional Notes: The research was supported by several grants at the Department of Mathematics, National University of Singapore
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 77 (2008), 1467-1494
  • MSC (2000): Primary 65M12; Secondary 76D05
  • DOI: https://doi.org/10.1090/S0025-5718-08-02087-5
  • MathSciNet review: 2398777