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

Quasi-optimal complexity of adaptive finite element method for linear elasticity problems in two dimensions
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摘要 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. 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.
出处 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2016年第2期151-168,共18页 应用数学和力学(英文版)
基金 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) the Construct Program of the Key Discipline in Hunan University of Science and Engineering
关键词 linear elasticity problem adaptive finite element method (AFEM) quasioptimal complexity linear elasticity problem, adaptive finite element method (AFEM), quasioptimal complexity
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