A maximum-principle preserving finite element method for scalar conservation equations

Handle URI:
http://hdl.handle.net/10754/597301
Title:
A maximum-principle preserving finite element method for scalar conservation equations
Authors:
Guermond, Jean-Luc; Nazarov, Murtazo
Abstract:
This paper introduces a first-order viscosity method for the explicit approximation of scalar conservation equations with Lipschitz fluxes using continuous finite elements on arbitrary grids in any space dimension. Provided the lumped mass matrix is positive definite, the method is shown to satisfy the local maximum principle under a usual CFL condition. The method is independent of the cell type; for instance, the mesh can be a combination of tetrahedra, hexahedra, and prisms in three space dimensions. © 2014 Elsevier B.V.
Citation:
Guermond J-L, Nazarov M (2014) A maximum-principle preserving finite element method for scalar conservation equations. Computer Methods in Applied Mechanics and Engineering 272: 198–213. Available: http://dx.doi.org/10.1016/j.cma.2013.12.015.
Publisher:
Elsevier BV
Journal:
Computer Methods in Applied Mechanics and Engineering
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Apr-2014
DOI:
10.1016/j.cma.2013.12.015
Type:
Article
ISSN:
0045-7825
Sponsors:
This material is based upon work 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 number FA9550-09-1-0424, FA99550-12-0358, and by Award No. 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.date.accessioned2016-02-25T12:30:12Zen
dc.date.available2016-02-25T12:30:12Zen
dc.date.issued2014-04en
dc.identifier.citationGuermond J-L, Nazarov M (2014) A maximum-principle preserving finite element method for scalar conservation equations. Computer Methods in Applied Mechanics and Engineering 272: 198–213. Available: http://dx.doi.org/10.1016/j.cma.2013.12.015.en
dc.identifier.issn0045-7825en
dc.identifier.doi10.1016/j.cma.2013.12.015en
dc.identifier.urihttp://hdl.handle.net/10754/597301en
dc.description.abstractThis paper introduces a first-order viscosity method for the explicit approximation of scalar conservation equations with Lipschitz fluxes using continuous finite elements on arbitrary grids in any space dimension. Provided the lumped mass matrix is positive definite, the method is shown to satisfy the local maximum principle under a usual CFL condition. The method is independent of the cell type; for instance, the mesh can be a combination of tetrahedra, hexahedra, and prisms in three space dimensions. © 2014 Elsevier B.V.en
dc.description.sponsorshipThis material is based upon work 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 number FA9550-09-1-0424, FA99550-12-0358, and by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherElsevier BVen
dc.subjectConservation equationsen
dc.subjectEntropy solutionsen
dc.subjectFirst-order viscosityen
dc.subjectParabolic regularizationen
dc.subjectUpwindingen
dc.titleA maximum-principle preserving finite element method for scalar conservation equationsen
dc.typeArticleen
dc.identifier.journalComputer Methods in Applied Mechanics and Engineeringen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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