Speaker

• Chiwang Shu (Brown University)

Mathematics Genealogy Project

• record 1
• record 2

Abstract

In these minicourses, we will give a general introduction to the discontinuous Galerkin (DG) methods for solving time-dependent, convection-dominated partial differential equations (PDEs), including the hyperbolic conservation laws, convection-diffusion equations, and PDEs containing higher-order spatial derivatives such as the KdV equations and other nonlinear dispersive wave equations.We will discuss cell entropy inequalities, nonlinear stability, and error estimates. The important ingredient of the design of DG schemes, namely the adequate choice of numerical fluxes, will be explained in detail. Issues related to the implementation of the DG method will also be addressed.

Lecture Notes

• Discontinuous Galerkin Methods for Convection Dominated PDEs
• Course note
• The development of discontinuous Galerkin methods
• Slide 1 , Slide 2
• Final Exam

Links

• course pages and videos
• Fengyan Li (Rensselaer Polytechnic Institute)
• Jingmei Qiu (University of Delaware)
  • Hyperbolic Conservation Laws and Numerical Methods: intoduction , hw 1 , hw 2 , hw 3, hw 4 , hw 5 , hw 6
• Luming Wang (UC Berkeley) : Discontinuous Galerkin Methods on Moving Domains with Large Deformations
• Jan S Hesthaven
• Bernardo Cockburn

Useful notes

• ENO and WENO programming
• Numerical Methods for Conservation Laws by Prof. Jan S. Hesthaven
  • Solution set 1 , Solution set 2 , Solution set 3 , Solution set 4 , Solution set 5
  • Solution set 6 , Solution set 7 , Solution set 8 , Solution set 9 , Solution set 10 , Solution set 11