Applied Mathematics and Mechanics >
Quasi-optimal complexity of adaptive finite element method for linear elasticity problems in two dimensions
Received date: 2015-06-26
Revised date: 2015-09-14
Online published: 2016-02-01
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
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.
Chunmei LIU, Liuqiang ZHONG, Shi SHU, Yingxiong XIAO . Quasi-optimal complexity of adaptive finite element method for linear elasticity problems in two dimensions[J]. Applied Mathematics and Mechanics, 2016 , 37(2) : 151 -168 . DOI: 10.1007/s10483-016-2041-9
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