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A Priori Error Analysis for Discretization of Sparse Elliptic Optimal Control Problems in Measure Space
2013
SIAM Journal of Control and Optimization
In this paper an optimal control problem is considered, where the control variable lies in a measure space and the state variable fulfills an elliptic equation. This formulation leads to a sparse structure of the optimal control. In this setting we prove a new regularity result for the optimal state and the optimal control. Moreover, a finite element discretization based on [E. Casas, C. Clason, and K. Kunisch, SIAM J. Control Optim., 50 (2012), pp. 1735-1752] is discussed and a priori error
doi:10.1137/120889137
fatcat:cgzwke26o5edfavkf5bv3xe4gy