Department of Mathematics

Speaker: Xinghui Zhong
Title: Wave Resolution Properties and Compact WENO Limiters for Discontinuous Galerkin Methods
Affiliation: University of Utah
Date: Monday, February 8, 2016
Place and Time: Room 101, Love Building, 3:35-4:30 pm
Refreshments: Room 204, Love Building, 3:00 pm

Abstract. Discontinuous Galerkin (DG) method is a class of finite element methods that has gained popularity in recent years due to its flexibility for arbitrarily unstructured meshes, with a compact stencil, and with the ability to easily accommodate arbitrary h-p adaptivity. However, some challenges still remain in specific application problems.

In the first part of my talk, we design compact limiters using weighted essentially non-oscillatory (WENO) methodology for DG methods solving hyperbolic conservation laws, with the goal of obtaining a robust and high order limiting procedure to simultaneously achieve uniform high order accuracy and sharp, non-oscillatory shock transitions. The main advantage of these compact limiters is their simplicity in implementation, especially on multi-dimensional unstructured meshes.

In the second part, using Fourier analysis, we provide a quantitative error analysis for the semi-discrete and fully discrete Runge-Kutta DG methods applied to time dependent wave equations. Based on these quantitative errors, we have computed the necessary number of points per wavelength required to obtain a fixed error. We also apply the same technique to study the superconvergence properties of DG methods.