The Local Discontinuous Galerkin Method for Flow and Transport Problems

Thursday, March 14, 2002 - 2:00pm - 3:00pm
Keller 3-180
Clint Dawson (The University of Texas at Austin)
Flow and transport problems are at the heart of most geoscience applications. These problems are characterized by rough coefficients, advection dominance, point sources and sinks, etc. Numerical schemes which preserve mass conservation and provide stable solutions in the presence of high gradients are desirable. In this talk, we will discuss a method recently proposed for handling these problems called the local discontinuous Galerkin method (LDG). This method is a type of classical mixed method, whereby one solves for the solution and its gradient or flux. This method is locally conservative, allows for local high order approximation, has built-in stability mechanisms such as upwinding, and allows for non-conforming mesh. Variants of the scheme will be discussed and applications to flow in porous media and shallow water will be presented.