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Becker, R., Kapp, H. and Rannacher, R. (2000) Adaptive Finite Element Methods for Optimal Control of Partial Differential Equations: Basic Concept. SIAM Journal on Control and Optimization, 39, 113-132.
https://doi.org/10.1137/S0363012999351097

has been cited by the following article:

• TITLE: Finite Volume Element Method for Solving the Elliptic Neumann Boundary Control Problems

  AUTHORS: Quanxiang Wang

  KEYWORDS: Finite Volume Element, Neumann Boundary Control, Variational Discretization

  JOURNAL NAME: Applied Mathematics, Vol.11 No.12, December 9, 2020

  ABSTRACT: Solving optimization problems with partial differential equations constraints is one of the most challenging problems in the context of industrial applications. In this paper, we study the finite volume element method for solving the elliptic Neumann boundary control problems. The variational discretization approach is used to deal with the control. Numerical results demonstrate that the proposed method for control is second-order accuracy in the L2 (Γ) and L∞ (Γ) norm. For state and adjoint state, optimal convergence order in the L2 (Ω) and H1 (Ω) can also be obtained.