Aktuelles
Einladung zum Vortrag von Herrn Prof. Dr. Thomas Führer am 09.10.2024 - 11:00 Uhr im Rahmen des Mathematischen Kolloquiums
[09.10.2024]Im Rahmen des Mathematischen Kolloquiums hält am Mittwoch, den 9. Oktober 2024, um 11:00 Uhr,
Herr Prof. Dr. Thomas Führer (Pontificia Universidad Católica de Chile, Santiago de Chile)
einen Vortrag zum Thema:
Space-time least-squares finite element methods
Der Vortrag findet im Raum E 408, Gebäude 3, statt.
Interessierte sind herzlich eingeladen.
Abstract:
In this talk we review some recent developments on space-time methods based on well-posed formulations of time-dependent PDEs. While variational formulations of elliptic PDEs often use the same solution and test space, this is different for time-dependent PDEs such as the heat equation and the wave equation. For the latter, the correct functional analytic setting is not clear in the literature. We consider the first-order system of the acoustic wave equation and prove that the operator corresponding to this system is an isomorphism from an appropriately defined graph space to the space of square-integrable functions. This novel well-posedness result paves the way to defining finite element methods of least- squares type on the space-time domain. The analysis uses some known stability results of weak and ultra-weak formulations of the second-order wave equation. Some numerical examples and discussion on future research conclude this talk.
This is a joint work with Roberto González and Michael Karkulik from Universidad Técnica Federico Santa María, Valparaíso, Chile and Gregor Gantner (University of Bonn).
