Optimal Control of Biharmonic Operator

Stefan Frei, Rolf Rannacher and Winnifried Wollner*

In this talk a priori error estimates are derived for the finite element discretization of optimal distributed control problems governed by the biharmonic operator. The state equation is discretized in primal mixed form using continuous piecewise biquadratic finite elements, while piecewise constant approximations are used for the control. The error estimates derived for the state variable as well as that for the control are order-optimal on general unstructured meshes. However, on uniform meshes not all error estimates are optimal due to the low-order control approximation. All theoretical results are confirmed by numerical tests.

Mathematics Subject Classification: 65N15 65N30 65N12 65K10

Keywords: Optimal distributed control; biharmonic operator; mixed finite elements; a priori error estimates

Minisymposion: Optimization of Mechanical Systems