VARIATIONAL DISCRETIZATION OF A CONTROL-CONSTRAINED PARABOLIC BANG-BANG OPTIMAL CONTROL PROBLEM

• 来源期刊: 计算数学（英文版）
• 关键词: Optimal control Heat equation Control constraints Finite elements A-priori error estimates Bang-bang controls
• 年，卷（期）: 2020,（1）
• 页码范围: 14-40
• 页数: 27页
• 语种: 英文
• DOI: 10.4208/jcm.1805-m2017-0171

摘要

We consider a control-constrained parabolic optimal control problem without Tikhonov term in the tracking functional.For the numerical treatment,we use variational discretization of its Tikhonov regularization:For the state and the adjoint equation,we apply Petrov-Galerkin schemes in time and usual conforming finite elements in space.We prove a-priori estimates for the error between the discretized regularized problem and the limit problem.Since these estimates are not robust if the regularization parameter tends to zero,we establish robust estimates,which depending on the problem's regularity-enhance the previous ones.In the special case of bang-bang solutions,these estimates are further improved.A numerical example confirms our analytical findings.