Past Event: Babuška Forum

An Automatically Stable FE Method With an Application to Shallow Water Modeling

Eirik Valseth, Postdoctoral Fellow, Computational Hydraulics Group, Oden Institute, UT Austin

Abstract

In this talk, we will introduce a novel stable finite element method for the numerical analysis of singular perturbation equations. The method derives its stability from optimal test functions as in the discontinuous Petrov-Galerkin method of Demkowicz and Gopalakrishnan. Hence, we are able to compute stable finite element approximations for any differential operator regardless of the mesh partition. Following the introduction for a linear scalar valued model problem, we consider the shallow water equations and present numerical verifications for commonly applied shallow water benchmark problems.

Biography

Eirik Valseth is a postdoctoral fellow in the Computational Hydraulics Group at the Oden Institute. His multidisciplinary research spans multiple disciplines including numerical analysis, material science, and fluid and solid mechanics. His current research at the Oden Institute focuses on the development of discontinuous Galerkin finite element methods as well as the coupling of continuous and discontinuous Galerkin methods for shallow water models.