An adaptive-order discontinuous Galerkin method for the solution of the Euler equations of gas dynamics

We present an adaptive-order discontinuous Galerkin technique that produces a compact, higher-order-accurate, and stable solver. The method involves a weak approximation of the conservation equations and a weak imposition of the Rankine-Hugoniot jump conditions across interelement and domain boundar ies. This discontinuous Galerkin approximation Is conservative and permits the use of different polynomial order in each subdomain according to the lo cal smoothness of the solution. Moreover, the compactness of the formulatio n makes possible a consistent and accurate implementation of boundary condi tions. Analytical studies of stability and numerical solutions of representative t wo- and three-dimensional problems suggest that the method is robust and ca pable of delivering high rates of convergence. Copyright (C) 2000 John Wile y & Sons, Ltd.