Space-time finite element methods for parabolic optimal control problems

Dr. Huidong Yang

Nov. 12, 2019, 2:30 p.m. S2 054

In this talk, we will present some numerical methods for optimal control of parabolic PDEs. In particular, we aim to minimize certain objective functionals subject to linear and nonlinear parabolic PDEs, and with proper constraints on the control variables. The objective functional may involve a Lipschitz continuous and convex but not Fréchet differentiable term, and lead to spatio-temporally sparse optimal control. The space-time finite element discretization of the optimality system, including both the state and adjoint state equations, relies on a Galerkin-Petrov variational formulation employing piecewise linear finite elements on unstructured simplicial space-time meshes. The nonlinear optimality system is solved by means of the semismooth Newton method, whereas the linearized coupled state and adjoint state systems are solved by an algebraic multigrid preconditioned GMRES method.

This is a joint work with Ulrich Langer (RICAM), Olaf Steinbach (TU Graz) and Fredi Tröltzsch (TU Berlin).