On reducing spurious oscillations in discontinuous Galerkin (DG) methods for steady-state convection-diffusion-reaction equations

A standard discontinuous Galerkin (DG) finite element method for discretizing steady-state convection–diffusion equations is known to be stable and to compute sharp layers in the convection-dominated regime, but also to show large spurious oscillations. This paper studies post-processing methods for reducing the spurious oscillations, which replace the DG solution in a vicinity of layers by a constant or linear approximation. Three methods from the literature are considered and several generalizations and modifications are proposed. Numerical studies with the post-processing methods are performed at two-dimensional examples