TY - JOUR
T1 - A Second-Order Maximum Principle Preserving Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations
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
Y1 - 2014/1
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
UR - http://www.scopus.com/inward/record.url?scp=84907032051&partnerID=8YFLogxK
U2 - 10.1137/130950240
DO - 10.1137/130950240
M3 - Article
SN - 0036-1429
VL - 52
SP - 2163
EP - 2182
JO - SIAM Journal on Numerical Analysis
JF - SIAM Journal on Numerical Analysis
IS - 4
ER -