We prove a sampling discretization theorem for the square norm of functions from finite dimensional subspace satisfying Nikol'skii's inequality with an upper bound on number points order dimension subspace.

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 al...