Mimetic Discretizations of Elliptic Control Problems
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- Antonietti, P.F., Bigoni, N. & Verani, M. J Sci Comput (2013) 56: 14. doi:10.1007/s10915-012-9659-7
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We investigate the performance of the Mimetic Finite Difference (MFD) method for the approximation of a constraint optimal control problem governed by an elliptic operator. Low-order and high-order mimetic discretizations are considered and a priori error estimates are derived, in a suitable discrete norm, for both the control and the state variables. A wide class of numerical experiments performed on a set of examples selected from the literature assesses the robustness of the MFD method and confirms the convergence analysis.