Optimal Control of the Laplace-Beltrami Operator on Compact Surfaces-Concept and Numerical Treatment
Year: 2012
Journal of Computational Mathematics, Vol. 30 (2012), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1111-m3678
Journal of Computational Mathematics, Vol. 30 (2012), Iss. 4 : pp. 392–403
Published online: 2012-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Elliptic optimal control problem Laplace-Beltrami operator Surfaces Control constraints Error estimates Semi-smooth Newton method.