TY - JOUR
T1 - Superconvergence of Finite Element Methods for Optimal Control Problems Governed by Parabolic Equations with Time-Dependent Coefficients
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 209
EP - 227
PY - 2018
DA - 2018/02
SN - 3
DO - http://doi.org/10.4208/eajam.030713.100813a
UR - https://global-sci.org/intro/article_detail/eajam/10919.html
KW - Superconvergence, finite element methods, optimal control problems,  parabolic equations, interpolation operator.
AB - <p style="text-align: justify;">In this article, a fully discrete finite element approximation is investigated for
constrained parabolic optimal control problems with time-dependent coefficients. The
spatial discretisation invokes finite elements, and the time discretisation a nonstandard
backward Euler method. On introducing some appropriate intermediate variables and
noting properties of the $L^2$ projection and the elliptic projection, we derive the superconvergence
for the control, the state and the adjoint state. Finally, we discuss some
numerical experiments that illustrate our theoretical results.</p>