2008-09 IAM PIMS MITACS Distinguished Colloquium-5

The success of the application of discontinuous Galerkin methods to nonlinear hyperbolic problems in the 1990s fueled the recent exploration of new and old DG methods for elliptic problems. Although the DG methods are clearly ideal for adaptive strategies, the method has been criticized, especially within the structural mechanics community, for having significantly more degrees of freedom than the continuous Galerkin method (for the same mesh) and for producing less accurate solutions than certain mixed methods. The hybridizable discontinuous Galerkin methods appeared as a response to this criticism. In this talk, we introduce these methods in the framework of second-order elliptic problems, show why they can be efficiently implemented and prove that they are actually more accurate than all previously known discontinuous Galerkin methods. Numerical comparisons with the continuous Galerkin method and with some mixed methods will be presented.