@Article{JCM-30-392, author = {}, 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 = {

We consider optimal control problems of elliptic PDEs on hypersurfaces $Γ$ in $\mathbb{R}^n$ 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1111-m3678}, url = {http://global-sci.org/intro/article_detail/jcm/8438.html} }