Recovery Type a Posteriori Error Estimates of Fully Discrete Finite Element Methods for General Convex Parabolic Optimal Control Problems
Year: 2012
Numerical Mathematics: Theory, Methods and Applications, Vol. 5 (2012), Iss. 4 : pp. 573–591
Abstract
This paper is concerned with recovery type a posteriori error estimates of fully discrete finite element approximation for general convex parabolic optimal control problems with pointwise 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 approximated by piecewise constant functions. We derive the superconvergence properties of finite element solutions. By using the superconvergence results, we obtain recovery type a posteriori error estimates. Some numerical examples are presented to verify the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2012.m1117
Numerical Mathematics: Theory, Methods and Applications, Vol. 5 (2012), Iss. 4 : pp. 573–591
Published online: 2012-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: General convex optimal control problems fully discrete finite element approximation a posteriori error estimates superconvergence recovery operator.