Error Estimates and Superconvergence of Mixed Finite Element Methods for Optimal Control Problems with Low Regularity
Year: 2012
Author: Yanping Chen, Tianliang Hou, Weishan Zheng
Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 6 : pp. 751–768
Abstract
In this paper, we investigate the error estimates and superconvergence property of mixed finite element methods for elliptic optimal control problems. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We derive $L^2$ and $L^\infty$-error estimates for the control variable. Moreover, using a recovery operator, we also derive some superconvergence results for the control variable. Finally, a numerical example is given to demonstrate the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.12-12S05
Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 6 : pp. 751–768
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Elliptic equations optimal control problems superconvergence error estimates mixed finite element methods.
Author Details
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