© 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 language||English (US)|
|Number of pages||20|
|Journal||SIAM Journal on Numerical Analysis|
|State||Published - Jan 2014|
Bibliographical noteKAUST 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.