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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

Topics at the IMA

School of Mathematics

University of Minnesota

Office: Vincent Hall 327

Lectures are at 2:30 pm, Wednesdays, Lind Hall 305 except for February 2

** 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:**

- 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
- April 6: Accuracy and superconvergence

4/6/2011 Video (flv) April 20: The effect of the nonconformity of the meshes

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)

4/20/2011 Video (flv) April 27: Convection-diffusion

May 4: Incompressible Navier-Stokes equations

May 11: Compressible Navier-Stokes equations

**References:**

- Bernardo Cockburn and C.-W. Shu,
*Runge-Kutta Discontinuous Galerkin Methods for convection-dominated 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.