A high accuracy NFEM for constrained optimal control problems governed by elliptic equations

In this paper, a new nonconforming finite element method (NFEM) is proposed for the constrained optimal control problems (OCPs) governed by elliptic equations. The state and co-state are approximated by the nonconforming EQ1rot element, and the control is approximated by the piecewise constant element, respectively. The superclose properties for the above three variables are obtained. Moreover, for the state and co-state, the superconvergence results are achieved in a broken energy norm by using the post-processing technique. Lastly, some numerical examples are provided to verify the theoretical analysis.