A SECOND-ORDER MAXIMUM PRINCIPLE PRESERVING LAGRANGE FINITE ELEMENT TECHNIQUE FOR NONLINEAR SCALAR CONSERVATION EQUATIONS

作者：Guermond Jean Luc^*; Nazarov Murtazo; Popov Bojan; Yang Yong

来源：SIAM Journal on Numerical Analysis, 2014, 52(4): 2163-2182.

DOI：10.1137/130950240

• conservation equations
• parabolic regularization
• entropy
• limiters
• entropy solutions
• finite element method

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.

• 出版日期2014