INVARIANT DOMAINS AND SECOND-ORDER CONTINUOUS FINITE ELEMENT APPROXIMATION FOR SCALAR CONSERVATION EQUATIONS Academic Article

abstract

• 2017 Society for Industrial and Applied Mathematics. We propose a technique for approximating nonlinear scalar conservation equations that uses continuous finite elements and is formally (at least) second-order accurate in space and maximum principle preserving. The method is explicit in time, uses unstructured continuous finite elements in space, and works in any space dimension. The stability and accuracy of the method are achieved by adapting the artificial viscosity.

authors

• Popov, Bojan

published proceedings

• SIAM JOURNAL ON NUMERICAL ANALYSIS

author list (cited authors)

• Guermond, J., & Popov, B.

citation count

• 29

complete list of authors

• Guermond, Jean-Luc||Popov, Bojan

publication date

• January 2017

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

published in

• SIAM Journal on Numerical Analysis  Journal

keywords

• Conservation Equations
• Entropy Viscosity
• Finite Element Method
• Limiters
• Maximum Principle
• Second-order Accuracy

Digital Object Identifier (DOI)

• 10.1137/16M1106560

start page

• 3120

end page

• 3146

volume

• 55

issue

• 6

URL

• http://dx.doi.org/10.1137/16m1106560