@Article{JCM-26-660, author = {}, title = {Superconvergence Analysis of Finite Element Methods for Optimal Control Problems of the Stationary Bénard Type}, journal = {Journal of Computational Mathematics}, year = {2008}, volume = {26}, number = {5}, pages = {660--676}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8650.html} }