Adaptive Space-Time Finite Element Methods for Parabolic Optimization Problems

In this paper we summerize recent results on a posteriori error estimation and adaptivity for space-time finite element discretizations of parabolic optimization problems. The provided error estimates assess the discretization error with respect to a given quantity of interest and separate the influences of different parts of the discretization (time, space, and control discretization). This allows us to set up an efficient adaptive strategy producing economical (locally) refined meshes for each time step and an adapted time discretization. The space and time discretization errors are equilibrated, leading to an efficient method. Mathematics Subject Classification (2000). 65N30, 49K20, 65M50, 35K55, 65N50.