TY - JOUR
T1 - Superconvergence Analysis of Finite Element Methods for Optimal Control Problems of the Stationary Bénard Type
AU - Yanzhen Chang & Danping Yang
JO - Journal of Computational Mathematics
VL - 5
SP - 660
EP - 676
PY - 2008
DA - 2008/10
SN - 26
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8650.html
KW - Optimal control problem, The stationary Bénard problem, Nonlinear coupled system, Finite element approximation, Superconvergence.
AB - <p style="text-align: justify;">In this paper, we consider the finite element approximation of the distributed optimal control problems of the stationary Bénard type under the pointwise control constraint. The states and the co-states are approximated by polynomial functions of lowest-order mixed finite element space or piecewise linear functions and the control is approximated by piecewise constant functions. We give the superconvergence analysis for the control; it is proved that the approximation has a second-order rate of convergence. We further give the superconvergence analysis for the states and the co-states. Then we derive error estimates in $L^\infty$-norm and optimal error estimates in $L^2$-norm.</p>