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

作     者：Chunmei LIU Liuqiang ZHONG Shi SHU Yingxiong XIAO 

作者机构：Institute for Computational Mathematics College of Science Hunan University of Science and Engineering School of Mathematical Sciences South China Normal University School of Mathematics and Computational Science Xiangtan University College of Civil Engineering and Mechanics Xiangtan University 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2016年第37卷第2期

页      面：151-168页

核心收录：

学科分类：07[理学] 0805[工学-材料科学与工程（可授工学、理学学位）] 070102[理学-计算数学] 0802[工学-机械工程] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

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 

主　　题：linear elasticity problem adaptive finite element method （AFEM） quasioptimal complexity 

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.