In this study, we present a precise anisotropic interpolation error estimate for the Morley finite element method (FEM) and apply it to fourth-order elliptic equations. We do not impose the shape-regularity mesh condition in the analysis. Anisotropic meshes can be used for this purpose. The main contributions of this study include providing a new proof of the term consistency. This enables us to obtain an anisotropic consistency error estimate. The core idea of the proof involves using the relationship between the Raviart--Thomas and Morley finite-element spaces. Our results indicate optimal convergence rates and imply that the modified Morley FEM may be effective for errors.

翻译：本研究针对Morley有限元方法提出了精确的各向异性插值误差估计，并将其应用于四阶椭圆方程。分析过程中未施加形状正则性网格条件，为此可采用各向异性网格。本研究的主要贡献包括：为项一致性提供了新的证明方法，从而获得各向异性一致性误差估计。证明的核心思想在于利用Raviart--Thomas有限元空间与Morley有限元空间之间的关联性。研究结果表明该方法具有最优收敛速率，并暗示改进的Morley有限元方法可能对误差控制具有良好效果。