# Adaptive space-time finite element methods for parabolic optimal control problems

## Andreas Schafelner

June 8, 2021, 3:30 p.m. ZOOM

We present, analyze, and test locally stabilized space-timefinite element methods on fully unstructured simplicial space-time meshes for the numerical solution of space-timetracking parabolic optimal control problems with the standard$L_2$-regularization. We derive a prior discretization error estimates in terms of the local mesh size. The adaptive versionis driven by local residual error indicators. We perform numerical tests for benchmark examples having different features. In particular, we consider a discontinuous target in the form of a first expanding and then contracting ball in 3Dthat is fixed in the 4D space-time cylinder.