A reconstructed central discontinuous Galerkin method for conservation laws

Central discontinuous Galerkin (CDG) methods are a family of high order numerical methods, which evolve two sets of numerical solutions defined on overlapping meshes and do not employ the numerical fluxes at element interfaces as in discontinuous Galerkin methods. However, evolving two sets of numerical solutions makes the CDG method relatively time-consuming. In this paper, we present a reconstructed central discontinuous Galerkin (RCDG) method for conservation laws. In this scheme, we reconstruct an approximate solution by projecting the numerical solution defined on the primal mesh into the approximate space defined on the dual mesh in the L2 sense. As a consequence, the reconstructed approximate solution plays a role as an alternative for the numerical solution defined on the dual mesh in the CDG method. Numerical examples demonstrate that the RCDG method is not only simpler and easier to implement than the CDG method but also reduces the computational cost considerably without sacrificing the high order accuracy of the CDG method.