2014/11/18 by Charles Brett, Andreas Dedner, Brett, C. +3 · 3 citations
Computer Science · Engineering · #65N15 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1411.4941
openalex publication_date 2014/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider an elliptic optimal control problem where the objective functional contains evaluations of the state at a finite number of points. In particular, we use a fidelity term that encourages the state to take certain values at these points, which means our problem is related to ones with state constraints at points. The analysis and numerical analysis differs from when the fidelity is in the L2 norm because we need the state space to embed into the space of continuous functions. In this paper we discretise the problem using two different piecewise linear finite element methods. For each discretisation we use two different approaches to prove a priori L2 error estimates for the control. We discuss the differences between these methods and approaches and present numerical results that agree with our analytical results.