# Space-Time Finite Element Methods for Parabolic Optimal Control Problems

## Dr. Huidong Yang

July 7, 2020, 1:30 p.m. ZOOM

In this talk, we will shortly summarize our recent work on space-time finite element methods for optimal control of parabolic equations. Three approaches are discussed by using $L^2$-regularization, $H^{-1}$-regularization, and $L^2$-regularization combined with $L^1$-norm of the control.

A space-time Petrov-Galerkin finite element discretization is used for the first-order necessary optimality system. The discretization is based on a variational formulation that employs piecewise linear finite elements simultaneously in space and time.

This is a joint work of Ulrich Langer (JKU/RICAM), Olaf Steinbach (TU Graz), Fredi Tröltzsch (TU Berlin).