Optimal Control of the Laplace-Beltrami operator on compact surfaces - concept and numerical treatment

Details Optimal Control of the Laplace-Beltrami operator on compact surfaces - concept and numerical treatment Optimal Control of the Laplace-Beltrami operator on compact surfaces - concept and numerical treatment

2011-01-07

arxiv.org/abs/1101.1385v1

Mathematics

Optimization and Control

Scientific paper

We consider optimal control problems of elliptic PDEs on hypersurfaces in 2- or 3-dimensional Euclidean space. The leading part of the PDE is given by the Laplace-Beltrami operator, which is discretized by finite elements on a polyhedral approximation of the surface. The discrete optimal control problem is formulated on the approximating surface and is solved numerically with a semismooth Newton algorithm. We derive optimal a priori error estimates for problems including control constraints and provide numerical examples confirming our analytical findings.

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