In this study, we present a precise anisotropic interpolation error estimate for the Morley finite element method (FEM) and apply it to fourth-order elliptical equations. We did not impose a shape-regularity mesh condition for the analysis. Therefore, anisotropic meshes can be used. The main contributions of this study include providing new proof of the consistency term. This enabled 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 show optimal convergence rates and imply that the modified Morley FEM may be effective for errors.

翻译：本研究提出了Morley有限元方法（FEM）在非各向同性插值误差下的精确估计，并将其应用于四阶椭圆方程。分析过程中未引入形状正则网格条件，因此可采用各向异性网格。本研究的主要贡献包括提供了一致性项的新证明，进而实现了各向异性一致性误差估计。该证明的核心思想在于利用Raviart--Thomas空间与Morley有限元空间之间的关联。研究结果表明，该方法达到了最优收敛速率，并暗示改进的Morley有限元方法可能在误差处理中具有有效性。