Error estimates for parabolic optimal control problem by fully discrete mixed finite element methods

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, whereas the time discretization is based on difference method...

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Bibliographic Details
Published in:Finite elements in analysis and design 2010-11, Vol.46 (11), p.957-965
Main Authors: Chen, Yanping, Lu, Zuliang
Format: Article
Language:English
Subjects:
A priori error estimates
Approximation
Calculus of variations and optimal control
Discretization
Errors
Estimates
Exact sciences and technology
Finite element method
Fully discrete mixed finite element methods
Gronwall's Lemma
Mathematical analysis
Mathematical models
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis. Scientific computation
Optimal control
Optimal control problem
Parabolic equations
Sciences and techniques of general use
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Summary: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, whereas 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.
ISSN:0168-874X
1872-6925
DOI:10.1016/j.finel.2010.06.011