A maximum-principle preserving finite element method for scalar conservation equations
KAUST Grant NumberKUS-C1-016-04
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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.
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.
SponsorsThis 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).