PhD comprehensive seminar | Tung Hoang, Post-processing and superconvergence for discontinuous Galerkin solutions

MC 6496

Speaker

Tung Hoang, Department of Applied Mathematics, University of Waterloo

Title

Post-processing and superconvergence for discontinuous Galerkin solutions

Abstract

Post-processing is used to enhance accuracy of numerical solutions of partial differential equations. Usually it is applied to the solution at the final time. Thus, it requires little computing time as compared with the cost of obtaining the numerical solution itself. For discontinuous  Galerkin methods applied to hyperbolic conservation laws B-spline based post-processing  increases accuracy from order k+1 to 2k+1 provided that the exact solution is smooth enough.  The post-processing is based on convolution of the numerical solution with a kernel defined in terms of these B-splines. The accuracy enhancement is based on the super accuracy of DG solution in the negative Sobolev norms. Extensive numerical experiments demonstrate the efficiency of this technique. In this seminar I will give a novel analysis of post-processing technique and connect post-processing to super accuracy of DG in the wave number approximation. Finally I will propose some questions for future investigation.