@Article{NMTMA-6-479, author = {}, 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 = {

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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2013.1133nm}, url = {http://global-sci.org/intro/article_detail/nmtma/5914.html} }