Space-time least squares finite elements for parabolic equations and applications

Michael Karkulik (USM Valpo) & Thomas Führer (PUC Santiago)

In the last couple of years, different space-time discretizations for parabolic problems have been proposed in the literature. In our talk, based on our recent work, we present a space-time least squares finite element method for the heat equation.

The advantages of our method over current space-time approaches is that we do not make any assumption on the space-time mesh (apart from the usual assumptions on spatial meshes), that our formulation is of Galerkin-type (which means that we do not have to worry about discrete inf-sup conditions), and that we have an a-posteriori error estimator for free. In particular, our approach features full space-time adaptivity.

We will present theory and numerical results.

We will meet in google meet, use the link below to connect with us on Friday:

Friday 27, March, via https://meet.google.com/viw-rqds-ikc