A Nonuniform Anisotropic FEM for Elliptic Boundary Layer Optimal Control Problems

Authors

Hongbo Guan, Zhengzhoug University of Light IndustryFollow
Yong Yang, Nanjing University of Aeronautics and AstronauticsFollow
Huiqing Zhu, University of Southern MississippiFollow

Document Type

Article

Publication Date

3-1-2021

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

In this paper, an anisotropic bilinear finite element method is con- structed for the elliptic boundary layer optimal control problems. Superclose- ness properties of the numerical state and numerical adjoint state in a ∈-norm are established on anisotropic meshes. Moreover, an interpolation type post- processed solution is shown to be superconvergent of order O(N-2), where the total number of nodes is of O(N2). Finally, numerical results are provided to verify the theoretical analysis.

Publication Title

Discrete and Continuous Dynamical Systems - Series B

Volume

26

Issue

3

First Page

1711

Last Page

1722

Recommended Citation

Guan, H., Yang, Y., Zhu, H. (2021). A Nonuniform Anisotropic FEM for Elliptic Boundary Layer Optimal Control Problems. Discrete and Continuous Dynamical Systems - Series B, 26(3), 1711-1722.
Available at: https://aquila.usm.edu/fac_pubs/18894