An Overview of Discontinuous Galerkin (DG) Methods for Elliptic Partial Differential

Abstract: This is a pedagogical talk providing an overview of two popular DG methods for elliptic partial differential equations (PDEs). While DG type methods are very popular for hyperbolic PDEs, many of the advantages of DG methods can be carried over to elliptic equations as well.

This talk features two methods with different backgrounds for formulation and analysis. The first method, called the interior penalty discontinuous method, is the generalization of the classical finite element method to discontinuous elements, while the second method, called the local discontinuous Galerkin method, extends the hyperbolic PDE construction and analysis to elliptic equations. The formal derivation, well-posedness of the discrete system, and error estimates of each method are discussed.

 

Speaker’s Bio: Stefan Schnake is a postdoctoral associate in the Multiscale Methods and Dynamics Group. He received his PhD in 2017 from the University of Tennessee. His research focuses on DG methods for linear and nonlinear elliptic partial differential equations and low rank approximations to solutions of partial differential equations.