Simultaneous space-time finite element methods for parabolic optimal control problems (Q2128453)

In this paper the reduced optimality system of the space-time tracking parabolic optimal control problem with \(L_2\)-regularization is discretized by a fully unstructured, space-time simplicial finite element. The space-time finite element method is implemented by means of the \textit{MFEM: Modular finite element methods library, (mfem.org)}. Numerical results are presented for two benchmarks. Optimal convergence rates are observed for the example with smooth solutions as predicted by the a priori estimates. Full space-time adaptivity is used in the case of a discontinuous target to obtain the full space-time solution. The large-scale system of space-time finite element equations is solved with a parallel version of the flexible GMRES preconditioned by a block-diagonal algebraic multigrid (AMG) method. For the entire collection see [Zbl 1484.65002].