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

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.