@Article{NMTMA-6-479,
author = {Tianliang Hou},
title = {Superconvergence and $L^∞$-Error Estimates of the Lowest Order Mixed Methods for Distributed Optimal Control Problems Governed by Semilinear Elliptic Equations},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2013},
volume = {6},
number = {3},
pages = {479--498},
abstract = {<p style="text-align: justify;">In this paper, we investigate the superconvergence property and the $L^∞$-error
estimates of mixed finite element methods for a semilinear elliptic control problem. 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 some superconvergence results for the control variable. Moreover, we derive $L^∞$-error estimates both for the control variable and the state variables. Finally, a
numerical example is given to demonstrate the theoretical results.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2013.1133nm},
url = {http://global-sci.org/intro/article_detail/nmtma/5914.html}
}