IMA Thematic Year on Simulating Our Complex World: Modeling, Computation and Analysis
MATH 8994: Discontinuous Galerkin Methods: An Introduction
Bernardo
Cockburn
School of Mathematics
University of
Minnesota
Office: Vincent Hall 327
Lectures are at 2:30 pm, Wednesdays,
Lind Hall 305 except for February 2
^{nd} lecture which is at 9:00
am.
Poster
Objective: This course is an introduction to the socalled
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:
 January 26: The original method: Linear scalar transport
 February 2: Linear, symmetric hyperbolic systems
2/2/2011 Video (flv)
 February 9: Nonlinear scalar conservation laws
2/9/2011 Video (flv)
 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)
 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: Convectiondiffusion
May 4: Incompressible NavierStokes equations
May 11: Compressible NavierStokes equations
References:
 Bernardo Cockburn and C.W. Shu, RungeKutta Discontinuous Galerkin
Methods for
convectiondominated problems, J. Sci. Comput. vol. 16 (2001),
pp. 173–261.

Bernardo Cockburn, Discontinuous Galerkin Methods, ZAMM Z. Angew. Math.
Mech.
vol. 83 (2003), pp. 731–754.
 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.
 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.