We present a precise anisotropic interpolation error estimate for the Morley finite element method and apply the estimate to fourth-order elliptic equations. We do not impose the shape-regularity mesh condition for analysis. Therefore, the use of anisotropic meshes is possible. The main contributions of this study include showing a new proof for the consistency term. This allows us to obtain an anisotropic consistency error estimate. The core idea of the proof involves using the relation between the Raviart--Thomas and Morley finite element spaces. Our results show the optimal convergence rates and imply that the modified Morley finite method may be effective regarding errors.
翻译：我们为莫尔利定点元素法提出了一个精确的厌食性内插误差估计,并将这一估计应用于第四阶椭圆形等离子方程。我们不强行规定形状常规网状条件进行分析。因此,使用动脉间流体是可能的。本研究的主要贡献包括为一致性术语展示新的证据。这使我们能够获得对动脉间一致性误差的估计。证据的核心概念涉及使用拉维亚-托马斯和莫利定点元素空间之间的关系。我们的结果显示了最佳的趋同率,并暗示修改的莫利定点方法可能对错误有效。
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