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

Andreas Schafelner

April 20, 2021, 1:30 p.m. ZOOM

We present, analyze, and test locally stabilized space-time finite element methods on fully unstructured simplicial space-time meshes for the numerical solution of space-time tracking 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 version is 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 3D that is fixed in the 4D space-time cylinder.