A Second-Order Maximum Principle Preserving Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations
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Abstract© 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.
CitationGuermond J-L, Nazarov M, Popov B, Yang Y (2014) A Second-Order Maximum Principle Preserving Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations. SIAM J Numer Anal 52: 2163–2182. Available: http://dx.doi.org/10.1137/130950240.
SponsorsThe 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).