Optimal control of interface problems with hp-finite elements

We investigate the optimal control of elliptic PDEs with jumping coefficients. As discretization we use interface concentrated finite elements on subdomains with smooth data. In order to apply convergence results, we prove higher regularity of the optimal solution using the concept of quasimonotone coefficients and a domain that is injective modulo polynomials of degree 1 at each vertex. Numerical results are presented for a semi-linear control problem with a non-local radiation operator, which models the production process of silicon carbide single crystals.