L∞-ESTIMATES OF MIXED FINITE ELEMENT METHODS FOR GENERAL NONLINEAR OPTIMAL CONTROL PROBLEMS

This paper investigates L∞--estimates for the general optimal control problems governed by two-dimensional nonlinear elliptic equations with pointwise control constraints using mixed finite element methods. The state and the co-state are approximated by the lowest order Raviart-Thomas mixed finite e...

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Bibliographic Details
Published in:Journal of systems science and complexity 2012-02, Vol.25 (1), p.105-120
Main Authors: Chen, Yanping, Lu, Zuliang
Format: Article
Language:English
Subjects:
Complex Systems
Control
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Statistics
Systems Theory
估计
函数近似
控制约束
最优控制问题
有限元空间
有限元逼近
混合有限元方法
非线性椭圆方程
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Summary:This paper investigates L∞--estimates for the general optimal control problems governed by two-dimensional nonlinear elliptic equations with pointwise control constraints using mixed finite element 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. The authors derive L∞--estimates for the mixed finite element approximation of nonlinear optimal control problems. Finally, the numerical examples are given.
ISSN:1009-6124
1559-7067
DOI:10.1007/s11424-011-9215-9