A Discontinuous Galerkin Method for Diffusion Based on Recovery

摘要

We present the details of the recovery-based DG method for 2-D diffusion problems on unstructured grids. In the recovery approach the diffusive fluxes are based on a smooth, locally recovered solution that in the weak sense is indistinguishable from the discontinuous discrete solution. This eliminates the introduction of ad hoc penalty or coupling terms found in traditional DG methods. Crucial is the choice of the proper basis for recovery of the smooth solution on the union of two elements. Some results on accuracy, stability and the range of eigenvalues are given, together with numerical solutions on rectangular grids.