OPTIMAL CONTROL OF THE LAPLACE-BELTRAMI OPERATOR ON COMPACT SURFACES: CONCEPT AND NUMERICAL TREATMENT

• 来源期刊: 计算数学（英文版）
• 关键词: Elliptic optimal control problem Laplace-Beltrami operator Surfaces Control constraints Error estimates Semi-smooth Newton method
• 年，卷（期）: 2012,（4）
• 页码范围: 392-403
• 页数: 12页
• 语种: 英文
• DOI: 10.4208/jcm.1111-m3678

摘要

We consider optimal control problems of elliptic PDEs on hypersurfaces Γ in Rn 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.