Morley finite element analysis for fourth-order elliptic equations under a semi-regular mesh condition

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.