Space-time finite element methods for parabolic optimal control problems

Dr. Huidong Yang

Nov. 12, 2019, 3:30 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 Fr\'{e}chet 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).