Error estimates for parabolic optimal control problem by fully discrete mixed finite element methods
Error estimates for parabolic optimal control problem by fully discrete mixed finite element methods
复制标题
全离散混合有限元法抛物型最优控制问题的误差估计
DOI：
10.1016/j.finel.2010.06.011
复制
发表时间：
2010-11-01
影响因子：
3.1
通讯作者：
Lu, Zuliang
中科院分区：
文献类型：
--
作者：
Chen, Yanping;Lu, Zuliang
本文研究了抛物线型方程二次凸最优控制问题的完全离散混合有限元方法。状态变量的空间离散采用常规的混合有限元方法，时间离散采用差分方法。状态和共状态用最低阶Raviart-Thomas混合有限元空间逼近，控制用分段常数函数逼近。应用标准混合有限元法的一些误差估计技术，导出了耦合状态和控制近似的先验误差估计。最后给出了一些数值算例，验证了理论结果。(C) 2010 Elsevier B.V.版权所有
In this paper we study the fully discrete mixed finite element methods for quadratic convex optimal control problem governed by parabolic equations. The space discretization of the state variable is done using usual mixed finite elements, where as the time discretization is based on difference methods. The state and the co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. By applying some error estimates techniques of standard mixed finite element methods, we derive a priori error estimates both for the coupled state and the control approximation. Finally, we present some numerical examples which confirm our theoretical results. (C) 2010 Elsevier B.V. All rights reserved.