85
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Global superconvergence analysis of a nonconforming FEM for Neumann boundary OCPs with elliptic equations

, &
Pages 2451-2461 | Received 25 Mar 2019, Accepted 03 Dec 2019, Published online: 02 Jan 2020
 

Abstract

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 EQ1rot 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 EQ1rot 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.

2010 Mathematics Subject Classifications:

Acknowledgements

The authors are grateful to the two anonymous referees for their helpful suggestions, which led to a clear presentation.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (No. 11501527), PhD Start-up Project of ZZULI (2015BSJJ070), Excellent Young Scholars Foundation of ZZULI (No. 2016XGGJS008).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.