On the connection of discontinuous Galerkin method and Godunov type methods of high order accuracy
It is shown that the schemes of discontinuous Galerkin method can be interpreted as a generalization of Godunov's method for piece wise polynomial functions. For the problem of interaction of a shock wave with entropy perturbation orders of accuracy close to second in the wake of the shock wave are obtained.
On the connection discontinuous Galerkin method and Godunov type methods of high order accuracy
Mathematical problems and theory of numerical methods