Solution limiters and flux limiters for high order discontinuous galerkin schemes

Abstract

We analyze a general concept of limiters for a high order DG scheme written for a 1-D problem. The limiters, which are local and do not require extended stencils, are incorporated into the solution reconstruction in order to meet the requirement of monotonicity and avoid spurious solution overshoots. A limiter β will be defined based on the solution jumps at grid interfaces. It will be shown that β should be 0 < β < 1 for a monotone approximate solution. © Springer-Verlag Berlin Heidelberg 2007.