Volume 5, Issue 4
Recovery Type A Posteriori Error Estimates of Fully Discrete Finite Element Methods for General Convex Parabolic Optimal Control Problems

Yuelong Tang & Yanping Chen

Numer. Math. Theor. Meth. Appl., 5 (2012), pp. 573-591.

Published online: 2012-05

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  • 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.

  • Keywords

General convex optimal control problems fully discrete finite element approximation a posteriori error estimates superconvergence recovery operator

  • AMS Subject Headings

35B37 49J20 65N30

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COPYRIGHT: © Global Science Press

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@Article{NMTMA-5-573, author = {Yuelong Tang and Yanping Chen}, title = {Recovery Type A Posteriori Error Estimates of Fully Discrete Finite Element Methods for General Convex Parabolic Optimal Control Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2012}, volume = {5}, number = {4}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2012.m1117}, url = {http://global-sci.org/intro/article_detail/nmtma/5950.html} }
TY - JOUR T1 - Recovery Type A Posteriori Error Estimates of Fully Discrete Finite Element Methods for General Convex Parabolic Optimal Control Problems AU - Yuelong Tang & Yanping Chen JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 573 EP - 591 PY - 2012 DA - 2012/05 SN - 5 DO - http://dor.org/10.4208/nmtma.2012.m1117 UR - https://global-sci.org/intro/article_detail/nmtma/5950.html KW - General convex optimal control problems KW - fully discrete finite element approximation KW - a posteriori error estimates KW - superconvergence KW - recovery operator AB -

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.

Yuelong Tang & Yanping Chen. (1970). Recovery Type A Posteriori Error Estimates of Fully Discrete Finite Element Methods for General Convex Parabolic Optimal Control Problems. Numerical Mathematics: Theory, Methods and Applications. 5 (4). 573-591. doi:10.4208/nmtma.2012.m1117
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