TY - JOUR
T1 - Superconvergence and $L^∞$-Error Estimates of the Lowest Order Mixed Methods for Distributed Optimal Control Problems Governed by Semilinear Elliptic Equations
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 479
EP - 498
PY - 2013
DA - 2013/06
SN - 6
DO - http://doi.org/10.4208/nmtma.2013.1133nm
UR - https://global-sci.org/intro/article_detail/nmtma/5914.html
KW - Semilinear elliptic equations, distributed optimal control problems, superconvergence,
$L^∞$-error estimates, mixed finite element methods.
AB - <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>