NUMERICAL APPROXIMATION OF THE ELLIPTIC EIGENVALUE PROBLEM BY STABILIZED NONCONFORMING FINITE ELEMENT METHOD

Zhifeng Weng; Shuying Zhai; Yuping Zeng; Xiaoqiang Yue

doi:10.11948/20200025

2021 Volume 11 Issue 3

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Zhifeng Weng, Shuying Zhai, Yuping Zeng, Xiaoqiang Yue. NUMERICAL APPROXIMATION OF THE ELLIPTIC EIGENVALUE PROBLEM BY STABILIZED NONCONFORMING FINITE ELEMENT METHOD[J]. Journal of Applied Analysis & Computation, 2021, 11(3): 1161-1176. doi: 10.11948/20200025

Citation:

Zhifeng Weng, Shuying Zhai, Yuping Zeng, Xiaoqiang Yue. NUMERICAL APPROXIMATION OF THE ELLIPTIC EIGENVALUE PROBLEM BY STABILIZED NONCONFORMING FINITE ELEMENT METHOD[J]. Journal of Applied Analysis & Computation, 2021, 11(3): 1161-1176. doi: 10.11948/20200025

NUMERICAL APPROXIMATION OF THE ELLIPTIC EIGENVALUE PROBLEM BY STABILIZED NONCONFORMING FINITE ELEMENT METHOD

1.
School of Mathematics Science, Huaqiao University, 362021 Quanzhou, China
2.
School of Mathematics, Jiaying University, 514015 Meizhou, China
3.
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education, School of Mathematics and Computational Science, Xiangtan University, 411105 Xiangtan, China

Corresponding author: Email address: yuexq@xtu.edu.cn (X. Yue)
Fund Project: The authors were supported by National Natural Science Foundation of China (11701197, 11701196, 11971414), Fundamental Research Funds for the Central Universities (ZQN-702), Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University (ZQN-YX502), Natural Science Foundation of Guangdong Province (2018A030307024) and Project of Scientific Research Fund of Hunan Provincial Science and Technology Department (2018WK4006)

Abstract

Abstract

In this paper, a stabilized nonconforming mixed finite element method is used to solve the elliptic eigenvalue problem. Firstly, the lower-equal order element is used to discretize the space combined with the stabilization term based on the velocity projection method, and the error analysis is given. Moreover, the upper and lower bounds of eigenvalues are obtained. Finally, numerical experiments are carried out to verify the effectiveness of the proposed method.
- Elliptic eigenvalue problem /
- stabilized nonconforming method /
- error estimate /
- lower and upper bounds
MSC: 65M60, 76D07, 65M12

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References

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