Optimal Control of the Laplace-Beltrami operator on compact surfaces - concept and numerical treatment
Optimization and Control
2011-01-10 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1101.1385,
title = {Optimal Control of the Laplace-Beltrami operator on compact surfaces - concept and numerical treatment},
author = {Michael Hinze and Morten Vierling},
journal= {arXiv preprint arXiv:1101.1385},
year = {2011}
}