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：本研究提出了莫利有限元法（Morley FEM）在各向异性网格下的精确插值误差估计，并将其应用于四阶椭圆方程。分析过程中未施加网格形状正则性条件，因此可采用各向异性网格。本研究的主要贡献在于提供了相容项的新证明方法，从而获得了各向异性相容误差估计。该证明的核心思想是利用Raviart–Thomas空间与莫利有限元空间之间的关系。研究结果表明，该方法达到了最优收敛速率，并暗示了改进的莫利有限元法可能对误差控制具有有效性。