A NEW FINITE ELEMENT APPROXIMATION OF A STATE-CONSTRAINED OPTIMAL CONTROL PROBLEM

• 来源期刊: 计算数学（英文版）
• 关键词: Optimal control problem State-constraints Fourth order variational inequalities Nonconforming finite elemerit method
• 年，卷（期）: 2009,（1）
• 页码范围: 97-114
• 页数: 18页
• 语种: 英文

摘要

In this paper,we study numerical methods for all optimal control problem with pointwise state constraints.The traditional approaches often need to deal with the deltasingularity in the dual equation.which causes many difficulties in its theoretical analysis and numerical approximation.In our new approach we reformulate the state-constrained optimal control as a constrained minimization problems only involving the state,whose optimality condition is characterized by a fourth order elliptic variational inequality.Then direct numerical algorithms (nonconforming finite element approximation)are proposed for the inequality,and error estimates of the finite element approximation are derived.Numerical experiments illustrate the effectiveness of the new approach.