@Article{JCM-30-392,
author = {Michael Hinze and Morten Vierling},
title = {Optimal Control of the Laplace-Beltrami Operator on Compact Surfaces-Concept and Numerical Treatment},
journal = {Journal of Computational Mathematics},
year = {2012},
volume = {30},
number = {4},
pages = {392--403},
abstract = {<p style="text-align: justify;">We consider optimal control problems of elliptic PDEs on hypersurfaces $Γ$ in $\mathbb{R}^n$&nbsp;for $n$=2, 3. The leading part of the PDE is given by the Laplace-Beltrami operator, which
is discretized by finite elements on a polyhedral approximation of $Γ$. The discrete optimal
control problem is formulated on the approximating surface and is solved numerically with
a semi-smooth Newton algorithm. We derive optimal a priori error estimates for problems
including control constraints and provide numerical examples confirming our analytical
findings.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1111-m3678},
url = {http://global-sci.org/intro/article_detail/jcm/8438.html}
}