Global Superconvergence Analysis of a Nonconforming FEM for Neumann Boundary OCPs With Elliptic Equations

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© 2020, © 2020 Informa UK Limited, trading as Taylor & Francis Group. In this paper, a nonconforming finite element method (FEM) is proposed for the Neumann type boundary optimal control problems (OCPs) governed by elliptic equations. The state and adjoint state are approximated by the nonconforming (Formula presented.) elements, and the control is approximated by the orthogonal projection through the adjoint state. Some superclose behaviors are derived by full use of the distinguish characters of this EQrot1 element, such as the interpolation operator equals to the Ritz projection, and the consistency error is higher than its interpolation error in the broken energy norm. After that, the global superconvergence results are obtained by employing the so-called post-interpolation technique. Finally, some numerical results are provided to verify the theoretical analysis.

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International Journal of Computer Mathematics

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