University of Texas at Austin

Upcoming Event: Oden Institute Seminar

Least-squares finite element methods for solving obstacle problems

Thomas Fuhrer, Associate Professor, Pontificia Universidad Católica de Chile

3:30 – 5PM
Thursday Nov 14, 2024

POB 6.304 and Zoom

Abstract

In this talk I present recent results on least-squares finite element methods for first-order reformulations of the elliptic and parabolic thick obstacle problem. As application for the elliptic case we consider elastic membranes constrained to lie over a rigid obstacle and for the parabolic case we consider American option pricing models as well as the one-phase Stefan problem.
Error estimates including the case of non-conforming convex sets are given and optimal convergence rates for sufficiently smooth solutions are shown. 
The coincidence set is a priorily unknown and for parabolic problems usually also evolves with time. Therefore, we study a posteriori bounds that can be used as error indicators in an adaptive algorithm to provide efficient numerical solution schemes.
Throughout this presentation we show numerical examples.

Biography

From 2004 to 2010, I studied Mathematics at the Technical University in Vienna where I also did my PhD from 2011 to 2014 under the supervision of Dirk Praetorius. In 2015 to 2016 I did a PostDoc at Catholic University of Chile working with Norbert Heuer. Since 2017 I am a Professor at the Catholic University of Chile. My main area of research is the numerical analysis of finite element methods for solving partial differential equations. I work on minimal residual methods such as the least-squares method and the discontinuous Petrov-Galerkin method.

Least-squares finite element methods for solving obstacle problems

Event information

Date
3:30 – 5PM
Thursday Nov 14, 2024
Hosted by Leszek F. Demkowicz