A Second-Order Maximum Principle Preserving Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations

Handle URI:
http://hdl.handle.net/10754/597402
Title:
A Second-Order Maximum Principle Preserving Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations
Authors:
Guermond, Jean-Luc; Nazarov, Murtazo; Popov, Bojan; Yang, Yong
Abstract:
© 2014 Society for Industrial and Applied Mathematics. This paper proposes an explicit, (at least) second-order, maximum principle satisfying, Lagrange finite element method for solving nonlinear scalar conservation equations. The technique is based on a new viscous bilinear form introduced in Guermond and Nazarov [Comput. Methods Appl. Mech. Engrg., 272 (2014), pp. 198-213], a high-order entropy viscosity method, and the Boris-Book-Zalesak flux correction technique. The algorithm works for arbitrary meshes in any space dimension and for all Lipschitz fluxes. The formal second-order accuracy of the method and its convergence properties are tested on a series of linear and nonlinear benchmark problems.
Citation:
Guermond J-L, Nazarov M, Popov B, Yang Y (2014) A Second-Order Maximum Principle Preserving Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations. SIAM J Numer Anal 52: 2163–2182. Available: http://dx.doi.org/10.1137/130950240.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Numerical Analysis
Issue Date:
Jan-2014
DOI:
10.1137/130950240
Type:
Article
ISSN:
0036-1429; 1095-7170
Sponsors:
The research of the authors was supported in part by the National Science Foundation grants DMS-1015984 and DMS-1217262, by the Air Force Office of Scientific Research, USAF, under grant/contract FA99550-12-0358, and by Award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
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Full metadata record

DC FieldValue Language
dc.contributor.authorGuermond, Jean-Lucen
dc.contributor.authorNazarov, Murtazoen
dc.contributor.authorPopov, Bojanen
dc.contributor.authorYang, Yongen
dc.date.accessioned2016-02-25T12:32:28Zen
dc.date.available2016-02-25T12:32:28Zen
dc.date.issued2014-01en
dc.identifier.citationGuermond J-L, Nazarov M, Popov B, Yang Y (2014) A Second-Order Maximum Principle Preserving Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations. SIAM J Numer Anal 52: 2163–2182. Available: http://dx.doi.org/10.1137/130950240.en
dc.identifier.issn0036-1429en
dc.identifier.issn1095-7170en
dc.identifier.doi10.1137/130950240en
dc.identifier.urihttp://hdl.handle.net/10754/597402en
dc.description.abstract© 2014 Society for Industrial and Applied Mathematics. This paper proposes an explicit, (at least) second-order, maximum principle satisfying, Lagrange finite element method for solving nonlinear scalar conservation equations. The technique is based on a new viscous bilinear form introduced in Guermond and Nazarov [Comput. Methods Appl. Mech. Engrg., 272 (2014), pp. 198-213], a high-order entropy viscosity method, and the Boris-Book-Zalesak flux correction technique. The algorithm works for arbitrary meshes in any space dimension and for all Lipschitz fluxes. The formal second-order accuracy of the method and its convergence properties are tested on a series of linear and nonlinear benchmark problems.en
dc.description.sponsorshipThe research of the authors was supported in part by the National Science Foundation grants DMS-1015984 and DMS-1217262, by the Air Force Office of Scientific Research, USAF, under grant/contract FA99550-12-0358, and by Award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectConservation equationsen
dc.subjectEntropyen
dc.subjectEntropy solutionsen
dc.subjectFinite element methoden
dc.subjectLimitersen
dc.subjectParabolic regularizationen
dc.titleA Second-Order Maximum Principle Preserving Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equationsen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Numerical Analysisen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
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