Error Estimates of Mixed Methods for Optimal Control Problems Governed by General Elliptic Equations
Year: 2016
Author: Tianliang Hou, Li Li
Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 6 : pp. 1050–1071
Abstract
In this paper, we investigate the error estimates of mixed finite element methods for optimal control problems governed by general elliptic equations. 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 $H^{-1}$-error estimates both for the control variable and the state variables. 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.2014.m807
Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 6 : pp. 1050–1071
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: General elliptic equations optimal control problems superconvergence error estimates mixed finite element methods.