discontinuous Galerkin method; reconstruction operator; nonlinear nonstationary scalar hyperbolic equation; Lipschitz-continuous boundary
This work is concerned with the introduction of a new numerical scheme based on the discontinuous Galerkin (DG) method. We propose to follow the methodology of higher order finite volume schemes and introduce a reconstruction operator into the DG scheme. This operator constructs higher order piecewise polynomial reconstructions from the lower order DG scheme. Such a procedure was proposed already in  based on heuristic arguments, however we provide a rigorous derivation, which justifies the increased order of accuracy. Numerical experiments are carried out.