A discontinuous Galerkin method using Taylor basis for computing shock waves on arbitrary grids

Abstract

The discontinuous Galerkin methods [1] (DGM) have recently become popular for the solution of systems of conservation laws to arbitrary order of accuracy. The DGM combine two advantageous features commonly associated to finite element and finite volume methods. As in classical finite element methods, accuracy is obtained by means of high-order polynomial approximation within an element rather than by wide stencils as in the case of finite volume methods. The physics of wave propagation is, however, accounted for by solving the Riemann problems that arise from the discontinuous representation of the solution at element interfaces.