On the connection of discontinuous Galerkin method and Godunov type methods of high order accuracy

Abstract: 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.Note: Research direction:Mathematical problems and theory of numerical method