Numerical Solution of the Euler Equations with a Multiorder Discontinuous Finite Element Method

Abstract

Discontinuous Galerkin methods have proven to be very well suited for the construction of robust high order accurate numerical schemes on arbitrary unstructured and possibly non conforming grids for a wide variety of applications. These accurate, flexibile and robust methods are however rather expensive in terms of computational cost. In this paper we propose to address the issue of computational efficiency of discontinuous finite element methods by introducing a “multiorder” discontinuous Galerkin solution strategy which is similar to a multigrid techinque but uses progressively lower order polynomial DG approximations on the same grid instead of the same discretization on progressively coarsened grids. We present the results obtained in the numerical solution of the Euler equations for the subsonic flow around a circle which give some indication of the effectiveness ot the proposed multiorder solution strategy.