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. 1 Introduction. Recently a number of new discretization methods have been developed to nu-merically solve modern problems of science and engineering. One of them is a Discontinuous Galerkin (DG) discretization scheme [3], which affords optimal orders of convergence for smooth problems by using high order approximatin