A nonuniform anisotropic FEM for elliptic boundary layer optimal control problems

In this paper, an anisotropic bilinear finite element method is constructed for the elliptic boundary layer optimal control problems. Supercloseness properties of the numerical state and numerical adjoint state in a \begin{document}$ \epsilon $\end{document} -norm are established on anisotropic meshes. Moreover, an interpolation type post-processed solution is shown to be superconvergent of order \begin{document}$ O(N^{-2}) $\end{document} , where the total number of nodes is of \begin{document}$ O(N^2) $\end{document} . Finally, numerical results are provided to verify the theoretical analysis.