A Type of Cascadic Adaptive Finite Element Method for Eigenvalue Problem

Authors

  • Fei Xu Beijing Institute for Scientific and Engineering Computing, Beijing University of Technology, Beijing 100124, China
  • Qiumei Huang College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
  • Shuangshuang Chen Beijing Institute for Scientific and Engineering Computing, College of Applied Sciences, Beijing University of Technology, Beijing 100124, China.
  • Hongkun Ma Sun Yat-Sen Business School, Sun Yat-Sen University, Guangzhou 510275, Guangdong, China and Zhuhai Financial Investment Group, Zhuhai 519031, Guangdong, China

DOI:

https://doi.org/10.4208/aamm.OA-2019-0054

Keywords:

Adaptive finite element method, cascadic multigrid method, eigenvalue problem, complementary method.

Abstract

In this paper, a type of cascadic adaptive finite element method is proposed for eigenvalue problem based on the complementary approach. In this new scheme, instead of solving the eigenvalue problem in each adaptive finite element space directly, we only need to do some smoothing steps for a boundary value problems on each adaptive space and solve some eigenvalue problems on a low dimensional space. Hence the efficiency can be improved since we do not need to solve the eigenvalue problems on each adaptive space which is time-consuming. Further, the complementary error estimate for eigenvalue problem will be introduced. This estimate can not only provide an accurate error estimate for eigenvalue problem but also provide the way to refine mesh and control the number of smoothing steps for the cascadic adaptive algorithm. Some numerical examples are presented to validate the efficiency of the proposed algorithm in this paper.

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Published

2020-04-10

Issue

Vol. 12 No. 3 (2020)

Section

Articles