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http://dx.doi.org/10.14317/jami.2013.479

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)
Publication Information
Journal of applied mathematics & informatics / v.31, no.3_4, 2013 , pp. 479-490 More about this Journal
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.
Keywords
A priori error estimates; superconvergence; variational discretization; optimal control problems; nonlinear equation;
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