Mathematics

We discuss distributed and boundary optimal control problems related to parabolic partial differential equations using a discontinuous Galerkin time stepping scheme. In particular, we focus on a Robin boundary optimal control problem for linear parabolic equations, on a distributed optimal control problem for the evolutionary Stokes equations and on some nonlinear optimal control problems arising from Biology. Stability and error estimates are presented for schemes of arbitrary order, under suitable regularity assumptions on the given data. Using suitable projection techniques, we also analyze the case of non-smooth initial data. Finally, we present numerical examples that verify our theoretical findings, and we discuss computational challenges involved in the numerical solution of the above systems.