Objective: This course is an introduction to the so-called discontinuous Galerkin (DG) methods for partial differential equations. The emphasis will be on the development of the methods for problems arising in fluid dynamics.

Lectures:

1. January 26: The original method: Linear scalar transport
2. February 2: Linear, symmetric hyperbolic systems
     2/2/2011 Video (flv)
3. February 9: Nonlinear scalar conservation laws
     2/9/2011 Video (flv)
4. February 16: The RKDG method for scalar conservation laws
     2/16/2011 Video (flv)
February 23: The RKDG method for gas dynamics
  2/23/2011 Video (flv) March 2: DG methods for diffusion problems
  3/2/2011 Video (flv) March 23: CANCELLED
March 30: Hybridizable methods: Static condensation
  3/30/2011 Video (flv)
5. April 6: Accuracy and superconvergence
     4/6/2011 Video (flv)
April 20: The effect of the nonconformity of the meshes
  4/20/2011 Video (flv) April 27: Convection-diffusion
May 4: Incompressible Navier-Stokes equations
May 11: Compressible Navier-Stokes equations

References:

1. Bernardo Cockburn and C.-W. Shu, Runge-Kutta Discontinuous Galerkin Methods for convection-dominated problems, J. Sci. Comput. vol. 16 (2001), pp. 173–261.
2. Bernardo Cockburn, Discontinuous Galerkin Methods, ZAMM Z. Angew. Math. Mech. vol. 83 (2003), pp. 731–754.
3. Bernardo Cockburn, Discontinuous Galerkin Methods for Computational Fluid Dynamics, Encyclopedia of Computational Mechanics vol. 3 (2004), pp. 91–123. Eds. E. Stein, R. de Borst and T.J.R. Hughes. John Wiley & Sons, Ltd., England.
4. N.C. Nguyen, J. Peraire and Bernardo Cockburn, Hybridizable discontinuous Galerkin methods, in LNSCE: Proceedings of the International Conference on Spectral and High Order Methods, Trondheim, Norway, Springer Verlag.