SIAM Journal on Numerical Analysis, Volume 59, Issue 2, Page 696-719, January 2021.
The adaptive nonconforming Morley finite element method approximates a regular solution to the von Kármán equations with optimal convergence rates for sufficiently fine triangulations and small bulk parameter in the Dörfler marking. This follows from the general axiomatic framework with the key arguments of stability, reduction, discrete reliability, and quasiorthogonality of an explicit residual-based error estimator. Particular attention is on the nonlinearity and the piecewise Sobolev embeddings required in the resulting trilinear form in the weak formulation of the nonconforming discretization. The discrete reliability follows with a conforming companion for the discrete Morley functions from the medius analysis. The quasiorthogonality also relies on a novel piecewise $H^1$ a priori error estimate and a careful analysis of the nonlinearity.

中文翻译：

---

具有最佳收敛速度的vonKármán方程的自适应Morley有限元法

SIAM数值分析学报，第59卷，第2期，第696-719页，2021年1月。
自适应非协调Morley有限元方法以最优的收敛速度逼近vonKármán方程的正则解，从而在Dörfler标记中具有足够精细的三角剖分和较小的体形参数。这是从一般公理框架得出的，其关键参数是基于残差的显式误差估计器的稳定性，减少性，离散可靠性和准正交性。特别要注意的是在不合格离散化的弱公式中，所产生的三线性形式的非线性和分段Sobolev嵌入。离散可靠性与来自medius分析的离散Morley函数的一致陪伴。准正交性还依赖于新颖的分段$ H ^ 1 $先验误差估计以及对非线性的仔细分析。