PhD comprehensive exam | Tung Hoang, Enhancing accuracy of discontinuous Galerkin solutions through post-processing

Enhancing accuracy of discontinuous Galerkin solutions through post-processing

Abstract

Post-processing for discontinuous Galerkin (DG) method is a technique used to enhance accuracy and smoothness of solutions of hyperbolic problems. Smoothness-increasing accuracy-conserving (SIAC) filters are a class of post-processing techniques in which we take a convolution of a DG solution with a kernel that is a linear combination of B-splines. Assuming that k is the order of polynomials in the finite element basis, we use a kernel that is a linear combination of 2k+1 B-splines of order k+1. In this case, we can increase the order of convergence of DG solutions of linear hyperbolic problems from k+1 to 2k+1, in the natural L2 norm. The SIAC filtering technique is very efficient in terms of computational cost since we only apply it to the DG solutions at the final time.

In this talk I will give an overview of the SIAC filtering technique, advantages of this technique and its limitations. Finally I will discuss some future works toward my thesis on post-processing for DG solutions of hyperbolic problems.