Discontinuous Galerkin method for hyperbolic equations with
singularities
February 13, 2013
3:00pm PGH 646
Abstract
Discontinuous Galerkin (DG) methods are finite element methods with
features from high resolution finite difference and finite volume
methodologies and are suitable for solving hyperbolic equations with
nonsmooth solutions. In this talk we will first give a survey on DG
methods, then we will describe our recent work on the study of DG methods
for solving hyperbolic equations with singularities in the initial
condition, in the source term, or in the solutions. The type of
singularities include both discontinuities and \(\delta\)-functions.
Especially for problems involving \(\delta\)-singularities, many numerical
techniques rely on modifications with smooth kernels and hence may severely
smear such singularities, leading to large errors in the approximation. On
the other hand, the DG methods are based on weak formulations and can be
designed directly to solve such problems without modifications, leading to
very accurate results. We will discuss both error estimates for model
linear equations and applications to nonlinear systems including the
rendez-vous systems and pressureless Euler equations involving
\(\delta\)-singularities in their solutions. This is joint work with Qiang
Zhang, Yang Yang and Dongming Wei.
Webmaster University of Houston
---
Last modified: April 11 2016 - 18:14:43