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

## Dr. Huidong Yang

July 7, 2020, 3:30 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).