A Priori Error Analysis for Discretization of Sparse Elliptic Optimal Control Problems in Measure Space | Zendy

Konstantin Pieper | Zendy; Boris Vexler | Zendy

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A Priori Error Analysis for Discretization of Sparse Elliptic Optimal Control Problems in Measure Space

Author(s) -

Konstantin Pieper,

Boris Vexler

Publication year - 2013

Publication title -

siam journal on control and optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.486

H-Index - 116

eISSN - 1095-7138

pISSN - 0363-0129

DOI - 10.1137/120889137

Subject(s) - mathematics , discretization , a priori and a posteriori , optimal control , measure (data warehouse) , finite element method , state space , variable (mathematics) , control variable , space (punctuation) , elliptic curve , state (computer science) , mathematical optimization , mathematical analysis , algorithm , computer science , statistics , philosophy , epistemology , database , operating system , physics , thermodynamics

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 estimates are derived, which significantly improve the estimates from that paper. Numerical examples for problems in two and three space dimensions illustrate our results.

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