Cell-centered discontinuous Galerkin discretizations for two-dimensional scalar conservation laws on unstructured grids and for one-dimensional Lagrangian hydrodynamics

We present cell-centered discontinuous Galerkin discretizations for two-dimensional scalar conservation laws on unstructured grids and also for the one-dimensional Lagrangian hydrodynamics up to third-order. We also demonstrate that a proper choice of the numerical fluxes allows to enforce stability properties of our discretizations.