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

Jean-Luc Guermond; Murtazo Nazarov; Bojan Popov; Yong Yang

doi:10.1137/130950240

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

Jean-Luc Guermond, Murtazo Nazarov, Bojan Popov, Yong Yang

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

63 Scopus citations

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.

Original language	English (US)
Pages (from-to)	2163-2182
Number of pages	20
Journal	SIAM Journal on Numerical Analysis
Volume	52
Issue number	4
DOIs	https://doi.org/10.1137/130950240
State	Published - Jan 2014
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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

abstract = "{\textcopyright} 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.",

author = "Jean-Luc Guermond and Murtazo Nazarov and Bojan Popov and Yong Yang",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: 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). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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AU - Guermond, Jean-Luc

AU - Nazarov, Murtazo

AU - Popov, Bojan

AU - Yang, Yong

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: 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). This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2014/1

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N2 - © 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.

AB - © 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.

UR - http://hdl.handle.net/10754/597402

UR - http://epubs.siam.org/doi/10.1137/130950240

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JF - SIAM Journal on Numerical Analysis

IS - 4

ER -

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

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