Quasi-optimal complexity of adaptive finite element method for linear elasticity problems in two dimensions |
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| Authors: | Chunmei Liu Liuqiang Zhong Shi Shu Yingxiong Xiao |
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| Institution: | 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 |
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| 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. |
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| Keywords: | linear elasticity problem adaptive finite element method (AFEM) quasioptimal complexity |
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