Upcoming Event: Oden Institute Seminar
Thomas Fuhrer, Associate Professor, Pontificia Universidad Católica de Chile
3:30 – 5PM
Thursday Nov 14, 2024
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.
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.