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Stability analysis of explicit entropy viscosity methods for non-linear scalar conservation equations


Authors: Andrea Bonito, Jean-Luc Guermond and Bojan Popov
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
Published electronically: October 3, 2013
MathSciNet review: 3167449
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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
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

DOI: https://doi.org/10.1090/S0025-5718-2013-02771-8
Keywords: Nonlinear conservation equations, finite elements, entropy, viscous approximation, stability, time stepping, strong stability preserving time stepping, Runge-Kutta
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)
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.