Year: 2020
Author: Fei Xu, Qiumei Huang, Shuangshuang Chen, Hongkun Ma
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 3 : pp. 774–796
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2019-0054
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 3 : pp. 774–796
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Adaptive finite element method cascadic multigrid method eigenvalue problem complementary method.