The local projection $P^0-P^1$-discontinuous-Galerkin finite element method for scalar conservation laws

Abstract

In this paper we introducé the Local Projection P° Pl-Discontinuous Galerkin finite elemente method (ÂI1P ° P l-scheme) for solving numencally scalar conservation laws This is an exphcit method obtained by modifying the expltcit Discontinuous Galerkin method introduced by G Chavent and G Salzano [3], via a simple local projection based on the monotomcity-preserving projections introduced by van Leer [13] The resulting scheme is an extension o f Godunov scheme that vérifies a local maximum pnnciple, and is TVDM (total variation diminishing in the means) Convergence to a weak solution is proven We display numencal évidence that the scheme is an entropy scheme of order one even when discontinuities are