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

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.

authors

• Popov, Bojan

published proceedings

• SIAM JOURNAL ON NUMERICAL ANALYSIS

author list (cited authors)

• Guermond, J., Nazarov, M., Popov, B., & Yang, Y.

citation count

• 54

complete list of authors

• Guermond, Jean-Luc||Nazarov, Murtazo||Popov, Bojan||Yang, Yong

publication date

• January 2014

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

published in

• SIAM Journal on Numerical Analysis  Journal

keywords

• Conservation Equations
• Entropy
• Entropy Solutions
• Finite Element Method
• Limiters
• Parabolic Regularization

Digital Object Identifier (DOI)

• 10.1137/130950240

URI

• https://hdl.handle.net/1969.1/183180

start page

• 2163

end page

• 2182

volume

• 52

issue

• 4

URL

• http%3A%2F%2Fdx.doi.org%2F10.1137%2F130950240