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

Jean-Luc Guermond; Murtazo Nazarov

doi:10.1016/j.cma.2013.12.015

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

Jean-Luc Guermond, Murtazo Nazarov

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

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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.

Original language	English (US)
Pages (from-to)	198-213
Number of pages	16
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	272
DOIs	https://doi.org/10.1016/j.cma.2013.12.015
State	Published - Apr 2014
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 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).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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Cite this

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title = "A maximum-principle preserving finite element method for scalar conservation equations",

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. {\textcopyright} 2014 Elsevier B.V.",

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doi = "10.1016/j.cma.2013.12.015",

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AU - Nazarov, Murtazo

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AB - 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.

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SP - 198

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JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

ER -

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

Abstract

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