Mid - Year Report Discontinuous Galerkin Euler Equation Solver

The focus of this effort is to produce a two dimensional inviscid, compressible flow solver using the Discontinuous Galerkin Finite Element approach. The Discontinuous Galerkin method seeks to project the exact solution onto a finite polynomial space while allowing for discontinuities at cell interfaces. This allows for the natural discontinuity capture that is required for a compressible flow solver. The appeal of the Discontinuous Galerkin Method is that it handles higher order spatial discretization without the use of larger stencils which is required in Finite Volume implementations.