Seminar in Numerical Analysis: Ira Neitzel (Universität Bonn)

On error estimates for optimal control problems with functions of bounded variation

joint work with Dominik Hafemeyer, Florian Mannel and Boris Vexler

We consider a convex optimal control problem governed by a partial differential equation in one space dimension which is controlled by a right-hand-side living in the space of functions with bounded variation. These functions tend to favor optimal controls that are piecewise constant with often finitely many jump poins. We are interested in deriving finite element discretization error estimates for the controls when the state ist discretized with usual piecewise linear finite elements, and the controls is either variationally discrete or piecwise constant. Due to the structure of the objective function, usual techniques for estimating the control error cannot be applied. Instead, these have to be derived from (suboptimal) error estimates for the state, which can later be improved.

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