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-orderaccurate, 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 boundaries. This discontinuous Galerkin approximation is conservative and permits the use of di!erent polynomial order in each subdomain according to the local smoothness of the solution. Moreover, the compactness of the formulation makes possible a consistent and accurate implementation of boundary conditions. Analytical studies of stability and numerical solutions of representative two- and three-dimensional problems suggest that the method is robust and capable of delivering high rates of convergence