Optimal control under reduced regularity

This paper deals with a linear quadratic optimal control problem with elliptic PDE constraints in three-dimensional domains with singularities. It is proved that the optimal control can be calculated by the finite element method at a rate of O(h2) provided that the mesh is sufficiently graded. The approximation of this control is computed from a piecewise constant approximation followed by a postprocessing step. Although the results are similar to the two-dimensional case, the proofs changed significantly.