TY - JOUR
T1 - Finite Element Approximation of Semilinear Parabolic Optimal Control Problems
AU - Hongfei Fu & Hongxing Rui
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 489
EP - 504
PY - 2011
DA - 2011/04
SN - 4
DO - http://doi.org/10.4208/nmtma.2011.m1020
UR - https://global-sci.org/intro/article_detail/nmtma/5980.html
KW - Finite element approximation, semilinear parabolic optimal control, pointwise control constraint, a priori error estimates.
AB - <p style="text-align: justify;">In this paper, the finite element
approximation of a class of semilinear parabolic optimal control
problems with pointwise control constraint is studied. We discretize
the state and co-state variables by piecewise linear continuous
functions, and the control variable is approximated by piecewise constant functions or piecewise linear discontinuous functions. Some $\textit{a priori}$ error estimates are derived for both the control
and state approximations. The convergence orders are also obtained.</p>