Quasi-optimal complexity of adaptive finite element method for linear elasticity problems in two dimensions

doi:10.1007/s10483-016-2041-9

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (2): 151-168.doi: https://doi.org/10.1007/s10483-016-2041-9

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Quasi-optimal complexity of adaptive finite element method for linear elasticity problems in two dimensions

Chunmei LIU¹, Liuqiang ZHONG², Shi SHU³, Yingxiong XIAO⁴

1. Institute for Computational Mathematics, College of Science, Hunan University of Science and Engineering, Yongzhou 425199, Hunan Province, China;
2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China;
3. School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan Province, China;
4. College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan 411105, Hunan Province, China

Received:2015-06-26 Revised:2015-09-14 Online:2016-02-01 Published:2016-02-01
Contact: Shi SHU E-mail:shushi@xtu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11201159, 11426102, and 11571293), the Natural Science Foundation of Hunan Province (No. 11JJ3135), the Foundation for Outstanding Young Teachers in Higher Education of Guangdong Province (No.Yq2013054), the Pearl River S&T Nova Program of Guangzhou (No. 2013J2200063), and the Construct Program of the Key Discipline in Hunan University of Science and Engineering

Abstract

Abstract:

This paper introduces an adaptive finite element method (AFEM) using the newest vertex bisection and marking exclusively according to the error estimator without special treatment of oscillation. By the combination of the global lower bound and the localized upper bound of the posteriori error estimator, perturbation of oscillation, and cardinality of the marked element set, it is proved that the AFEM is quasi-optimal for linear elasticity problems in two dimensions, and this conclusion is verified by the numerical examples.

Key words: linear elasticity problem, adaptive finite element method (AFEM), quasioptimal complexity

2010 MSC Number:

74S05
74B05

Chunmei LIU, Liuqiang ZHONG, Shi SHU, Yingxiong XIAO. Quasi-optimal complexity of adaptive finite element method for linear elasticity problems in two dimensions. Applied Mathematics and Mechanics (English Edition), 2016, 37(2): 151-168.

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References

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Quasi-optimal complexity of adaptive finite element method for linear elasticity problems in two dimensions

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