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：本文对Morley有限元方法提出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。分析中未施加形状正则网格条件，因此可使用各向异性网格。本研究的主要贡献包括给出相容项的新证明，从而获得各向异性相容性误差估计。证明的核心思想是利用Raviart-Thomas与Morley有限元空间之间的关系。研究结果表明该方法具有最优收敛速率，并说明修正的Morley有限元方法在误差控制方面具有有效性。