Optimal Accuracy of Discontinuous Galerkin for Diffusion

The Recovery-based Discontinuous Galerkin method (RDG) for linear diusion-shear problems is shown on triangles to achieve the order of accuracy 2p + 2 for even p and 2p for odd p, where p 1 is the order of the polynomial basis used. The RDG method incorporates a solution-enhancement step that reuses the recovery results, and an extra recovery step based on the enhanced solution. Thus, the stencil is extended not only to an element’s face-sharing neighbors but also to the vertex-sharing ones. The order-of-accuracy results are obtained with Fourier analysis on a grid of structured right triangles.