TY - JOUR
T1 - Optimal Control of the Laplace-Beltrami Operator on Compact Surfaces-Concept and Numerical Treatment
AU - Michael Hinze & Morten Vierling
JO - Journal of Computational Mathematics
VL - 4
SP - 392
EP - 403
PY - 2012
DA - 2012/08
SN - 30
DO - http://doi.org/10.4208/jcm.1111-m3678
UR - https://global-sci.org/intro/article_detail/jcm/8438.html
KW - Elliptic optimal control problem, Laplace-Beltrami operator, Surfaces, Control
constraints, Error estimates, Semi-smooth Newton method.
AB - <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>