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

Andrea Bonito; Jean-Luc Guermond; Bojan Popov

doi:10.1090/s0025-5718-2013-02771-8

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

Andrea Bonito, Jean-Luc Guermond, Bojan Popov

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

We establish the L2-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. © 2013 American Mathematical Society.

Original language	English (US)
Pages (from-to)	1039-1062
Number of pages	24
Journal	Mathematics of Computation
Volume	83
Issue number	287
DOIs	https://doi.org/10.1090/s0025-5718-2013-02771-8
State	Published - Oct 3 2013
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: 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)
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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abstract = "We establish the L2-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. {\textcopyright} 2013 American Mathematical Society.",

author = "Andrea Bonito and Jean-Luc Guermond and Bojan Popov",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: 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) This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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doi = "10.1090/s0025-5718-2013-02771-8",

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AU - Bonito, Andrea

AU - Guermond, Jean-Luc

AU - Popov, Bojan

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: 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) This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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Y1 - 2013/10/3

N2 - We establish the L2-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. © 2013 American Mathematical Society.

AB - We establish the L2-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. © 2013 American Mathematical Society.

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EP - 1062

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 287

ER -

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

Abstract

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