Mimetic Discretizations of Elliptic Control Problems

Authors:
Paola F. Antonietti;Nadia Bigoni;Marco Verani
Affiliations:
MOX, Dipartimento di Matematica, Politecnico di Milano, Milan, Italy 20133;MOX, Dipartimento di Matematica, Politecnico di Milano, Milan, Italy 20133;MOX, Dipartimento di Matematica, Politecnico di Milano, Milan, Italy 20133
Venue:
Journal of Scientific Computing
Year:
2013

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Abstract

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.