报告摘要：
| This talk is devoted to the quasi-optimal convergence analysis of a family of adaptive high order nonconforming elements, which includes the Lin-Tobiska-Zhou element as its lowest order element. Different to the nonconforming $P_1$ element (Crouzeix-Raviart element), the gradient of the discrete solution considered in this paper is not a piecewise constant vector. New quasi-orthogonality and new discrete upper bound are established for the first time. Based on them, convergence of the adaptive algorithm using standard D"{o}rfler collective marking strategy and quasi-optimality results are eventually established. Numerical experiments confirm theoretical results.
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