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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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Stability analysis of explicit entropy viscosity methods for non-linear scalar conservation equations
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by Andrea Bonito, Jean-Luc Guermond and Bojan Popov PDF
Math. Comp. 83 (2014), 1039-1062 Request permission

Abstract:

We establish the $L^2$-stability of an entropy viscosity technique applied to nonlinear scalar conservation equations. First- and second-order explicit time-stepping techniques using continuous finite elements in space are considered. The method is shown to be stable independently of the polynomial degree of the space approximation under the standard CFL condition.
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Additional Information
  • Andrea Bonito
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
  • MR Author ID: 783728
  • Email: bonito@math.tamu.edu).
  • Jean-Luc Guermond
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843. On leave from LIMSI, UPRR 3251 CNRS, BP 133, 91403 Orsay Cedex, France
  • Email: guermond@math.tamu.edu
  • Bojan Popov
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
  • Email: popov@tamu.edu
  • Received by editor(s): January 27, 2012
  • Received by editor(s) in revised form: October 12, 2012
  • Published electronically: October 3, 2013
  • Additional Notes: This material is based upon work supported by the Department of Homeland Security under agreement 2008-DN-077-ARI018-02, National Science Foundation grants DMS-0811041, DMS-0914977, DMS-1015984, AF Office of Scientific Research grant FA99550-12-0358, and is partially supported by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST)
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 83 (2014), 1039-1062
  • MSC (2010): Primary 35F25, 65M12, 65N30, 65N22
  • DOI: https://doi.org/10.1090/S0025-5718-2013-02771-8
  • MathSciNet review: 3167449