TY - JOUR
T1 - Error Estimates of Mixed Methods for Optimal Control Problems Governed by General Elliptic Equations
AU - Hou , Tianliang
AU - Li , Li
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1050
EP - 1071
PY - 2018
DA - 2018/05
SN - 8
DO - http://doi.org/10.4208/aamm.2014.m807
UR - https://global-sci.org/intro/article_detail/aamm/12131.html
KW - General 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 of mixed finite element
methods for optimal control problems governed by general elliptic equations. 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 $H^{-1}$-error estimates both for the control variable and the state
variables. Finally, a numerical example is given to demonstrate the theoretical results.</p>