The article deals with the analysis of a nonconforming finite element method for the discretization of optimization problems governed by variational inequalities. The state and adjoint variables are discretized using Crouzeix–Raviart nonconforming finite elements, and the control is discretized using a variational discretization approach. Error estimates have been established for the state and control variables. The results of numerical experiments are presented.
Funding statement: The third author was partially supported by the Simons Foundation and the Oberwolfach Research Institute for Mathematics.
A part of the work was completed during the research stay of the second and third authors in the Oberwolfach Research Institute for Mathematics.
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