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 journalArticlepeer-review

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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 languageEnglish (US)
Pages (from-to)2163-2182
Number of pages20
JournalSIAM Journal on Numerical Analysis
Volume52
Issue number4
DOIs
StatePublished - Jan 2014
Externally publishedYes

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