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

Jean-Luc Guermond, Murtazo Nazarov

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

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 languageEnglish (US)
Pages (from-to)198-213
Number of pages16
JournalComputer Methods in Applied Mechanics and Engineering
Volume272
DOIs
StatePublished - Apr 2014
Externally publishedYes

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