Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (6): 1542-1554.

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Error Estimates for the Finite Element Approximation of Nonlinear Parabolic Optimal Control Problems

 FU Hong-Fei1, RUI Hong-Xing2   

  1. 1.School of Mathematics and Computational Science, China University of Petroleum, Shandong Dongying 257061|2.School of Mathematics, Shandong University, Jinan 250100
  • Received:2008-08-27 Revised:2009-10-16 Online:2010-12-25 Published:2010-12-25
  • Supported by:

    国家基础研究项目(2007CB814906)和国家自然科学基金(10771124)资助

Abstract:

In this paper, the finite element approximation to a class of nonlinear optimal control problems with two different kinds of control constrained sets is investigated, where the state and co-state variables are discretized by piecewise linear continuous functions and the control variable is approximated by piecewise constant functions. Some a priori error estimates are derived for both control and state approximations.
It is proven that these approximations have convergence order O(hU+h+k), where hU and h are the spatial mesh-sizes for control and state, respectively, and k is the time increment. Numerical examples are given to show the efficiency of the present scheme.

Key words: Finite element approximation, Nonlinear optimal control, Priori error estimates

CLC Number: 

  • 49J20
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