Abstract: We introduce the hybridizable discontinuous Galerkin (HDG) methods in the framework of steady-state diffusion problems and show why they can be implemented more efficiently than any other DG method and why they are also more accurate. We then give an overview of the application of these methods to several problems including wave propagation, linear and nonlinear elasticity, convection-diffusion and the incompressible and compressible Navier-Stokes equations.
Biography: Dr. Cockburn received his PhD from the University of Chicago in 1986 under the direction of Jim Douglas, Jr. Since 1987, he has worked at the School of Mathematics at the University of Minnesota. In 2010, he was an Invited Speaker at the International Congress of Mathematicians. He is an ISIS Highly Cited author as well as a McKnight Distinguished University Professor. In addition, he is a Chair Professor at the Department of Mathematics and Statistics of King Fahd University of Petroleum and Minerals. Dr. Cockburn is best known for work on discontinuous Galerkin methods for partial differential equations. More information about Dr. Cockburn can be found at http://www.math.umn.edu/~cockburn/.