Numerical analysis for the approximation of optimal control problems with pointwise observations |
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| Authors: | Lili Chang Wei Gong Ningning Yan |
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| Affiliation: | 1. Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China;2. LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China;3. NCMIS & LSEC, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China |
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| Abstract: | 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. |
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| Keywords: | optimal control problems pointwise observations finite element method a priori error estimate a posteriori error estimate |
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