TY - JOUR
T1 - Error Estimates and Superconvergence of RT0 Mixed Methods for a Class of Semilinear Elliptic Optimal Control Problems
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 637
EP - 656
PY - 2013
DA - 2013/06
SN - 6
DO - http://doi.org/10.4208/nmtma.2013.1230nm
UR - https://global-sci.org/intro/article_detail/nmtma/5923.html
KW - Semilinear elliptic equations, optimal control problems, superconvergence, error estimates, mixed finite element methods.
AB - <p style="text-align: justify;">In this paper, we will investigate the error estimates and the
superconvergence property of mixed finite element methods for a
semilinear elliptic control problem with an integral constraint on
control. The state and co-state are approximated by the lowest order
Raviart-Thomas mixed finite element and the control variable
is approximated by piecewise constant functions. We derive some
superconvergence properties for the control variable and the state
variables. Moreover, we derive $L^∞$- 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.</p>