Superconvergence analysis of a nonconforming finite element method for monotone semilinear elliptic optimal control problems |
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Authors: | Hongbo Guan Dongyang Shi |
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Affiliation: | 1. College of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou, China;2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, China |
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Abstract: | A nonconforming finite element method (FEM) is proposed for optimal control problems (OCPs) governed by monotone semilinear elliptic equations. The state and adjoint state are approximated by the nonconforming elements, and the control is approximated by the orthogonal projection of the adjoint state, respectively. Some global supercloseness and superconvergence estimates are achieved by making full use of the distinguish characters of this element, such as the interpolation equals to its Ritz projection, and the consistency error is 1 − ε ( is small enough) order higher than its interpolation error in the broken energy norm when the exact solution belongs to H3 − ε(Ω). Finally, some numerical results are presented to verify the theoretical analysis. |
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Keywords: | nonconforming element semilinear OCPs supercloseness and superconvergence |
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