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。我们未对网格施加形状正则性条件，因此允许使用各向异性网格。主要贡献包括对相容项给出了新的证明，从而获得了各向异性相容误差估计。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。数值结果表明该方法能达到最优收敛阶，并说明修正的Morley有限元方法对误差分析具有有效性。