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Numerical analysis for the approximation of optimal control problems with pointwise observations
Author(s) -
Chang Lili,
Gong Wei,
Yan Ningning
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2861
Subject(s) - pointwise , mathematics , discretization , optimal control , a priori and a posteriori , piecewise , piecewise linear function , state (computer science) , adjoint equation , numerical analysis , mathematical optimization , mathematical analysis , partial differential equation , algorithm , philosophy , epistemology
In this paper, we study the numerical methods for optimal control problems governed by elliptic PDEs with pointwise observations of the state. The first order optimality conditions as well as regularities of the solutions are derived. The optimal control and adjoint state have low regularities due to the pointwise observations. For the finite dimensional approximation, we use the standard conforming piecewise linear finite elements to approximate the state and adjoint state variables, whereas variational discretization is applied to the discretization of the control. A priori and a posteriori error estimates for the optimal control, the state and adjoint state are obtained. Numerical experiments are also provided to confirm our theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.