TY - JOUR
T1 - A maximum-principle preserving finite element method for scalar conservation equations
AU - Guermond, Jean-Luc
AU - Nazarov, Murtazo
N1 - 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.
PY - 2014/4
Y1 - 2014/4
N2 - 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.
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.
UR - http://hdl.handle.net/10754/597301
UR - https://linkinghub.elsevier.com/retrieve/pii/S0045782514000024
UR - http://www.scopus.com/inward/record.url?scp=84893449924&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2013.12.015
DO - 10.1016/j.cma.2013.12.015
M3 - Article
SN - 0045-7825
VL - 272
SP - 198
EP - 213
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
ER -