TY - JOUR
T1 - Error Estimates and Superconvergence of Mixed Finite Element Methods for Optimal Control Problems with Low Regularity
AU - Chen , Yanping
AU - Hou , Tianliang
AU - Zheng , Weishan
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 751
EP - 768
PY - 2012
DA - 2012/12
SN - 4
DO - http://doi.org/10.4208/aamm.12-12S05
UR - https://global-sci.org/intro/article_detail/aamm/147.html
KW - Elliptic equations, optimal control problems, superconvergence, error estimates,
mixed finite element methods.
AB - <p style="text-align: justify;">In this paper, we investigate the error estimates and
superconvergence property of mixed finite element methods for
elliptic optimal control problems. 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 $L^\infty$-error
estimates for the control variable. Moreover, using a recovery
operator, we also derive some superconvergence results for the
control variable. Finally, a numerical example is given to
demonstrate the theoretical results.</p>