A posteriori error estimates for mixed finite element approximation of nonlinear quadratic optimal control problems

Abstract

In this paper, we obtain an a posteriori error analysis for mixed finite element approximation of convex optimal control problems governed by a nonlinear second-order elliptic equation. Our results are based on the approximation for both the coupled state variables and the control variable. We propose to improve the error estimates, which can be used to construct an adaptive finite element scheme. A numerical example demonstrating our theoretical results is also presented in this paper.

Keywords:

• nonlinear quadratic optimal control problems
• mixed finite element approximation; a posteriori error estimates

1991 Mathematics Subject Classifications: :

• 49J20
• 65N30

Acknowledgements

The authors express their thanks to the referees for their helpful suggestions, which led to improvements of the presentation.This work is supported by Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme (2008), National Science Foundation of China (10971074), Specialized Research Fund for the Doctoral Program of Higher Education (20114407110009), and China Postdoctoral Science Foundation (2011M500968).