On reducing spurious oscillations in discontinuous Galerkin (DG) methods for steady-state convection-diffusion 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. (c) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper studies post-processing methods to reduce spurious oscillations in discontinuous Galerkin finite element method, which involve replacing the DG solution near layers with constant or linear approximations. Numerical studies confirm the effectiveness of these post-processing methods.