Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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A PRIORI ERROR ESTIMATES AND SUPERCONVERGENCE PROPERTY OF VARIATIONAL DISCRETIZATION FOR NONLINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS

  • Tang, Yuelong (Department of Mathematics and Computational Science, Hunan University of Science and Engineering) ;
  • Hua, Yuchun (Department of Mathematics and Computational Science, Hunan University of Science and Engineering)
  • Received : 2012.07.16
  • Accepted : 2012.10.27
  • Published : 2013.05.30
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Abstract

In this paper, we investigate a priori error estimates and superconvergence of varitional discretization for nonlinear parabolic optimal control problems with control constraints. The time discretization is based on the backward Euler method. The state and the adjoint state are approximated by piecewise linear functions and the control is not directly discretized. We derive a priori error estimates for the control and superconvergence between the numerical solution and elliptic projection for the state and the adjoint state and present a numerical example for illustrating our theoretical results.

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References

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