SIAM Journal on Numerical Analysis, Volume 59, Issue 3, Page 1195-1217, January 2021.
A shear-locking free finite element discretization of the Reissner--Mindlin plate model is introduced. The rotation is discretized with piecewise polynomials of degree $k+2$ while the degree $k\geq0$ is used for the displacement gradient. The method is closely related to the (generalized) Taylor--Hood pairing. In this case the general theory of saddle-point problems with penalty cannot exclude that the convergence speed for the rotation is limited by the lower rate expected for the displacement. However, in this paper, it is shown that the rotations are approximated at optimal order of accuracy. This superconvergence phenomenon is proved by means of the approximation properties of the Fortin operator for the Taylor--Hood element and the Galerkin projection.

中文翻译：

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Reissner-Mindlin平板的泰勒-霍德离散化

SIAM数值分析学报，第59卷，第3期，第1195-1217页，2021年1月。
介绍了Reissner-Mindlin板模型的无剪切锁定的有限元离散化方法。旋转用度数$ k + 2 $的分段多项式离散化，而度数$ k \ geq0 $用于位移梯度。该方法与（广义）泰勒-胡德配对紧密相关。在这种情况下，带有罚分的鞍点问题的一般理论不能排除旋转的收敛速度受到位移期望的较低速率的限制。然而，在本文中，表明旋转是按最佳精度顺序近似进行的。通过Fortin算子对Taylor-Hood元素和Galerkin投影的逼近性质证明了这种超收敛现象。