TY - JOUR T1 - Finite Element Approximation of Semilinear Parabolic Optimal Control Problems 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 -

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.