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 ...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.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.1120115911426102+4 种基金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
文摘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.
