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In this study, we present a precise anisotropic interpolation error estimatefor the Morley finite element method (FEM) and apply it to fourth-orderelliptical equations. We did not impose a shape-regularity mesh condition forthe analysis. Therefore, anisotropic meshes can be used. The main contributionsof this study include providing new proof of the consistency term. This enabledus to obtain an anisotropic consistency error estimate. The core idea of theproof involves using the relationship between the Raviart--Thomas and Morleyfinite element spaces. Our results show optimal convergence rates and implythat the modified Morley FEM may be effective for errors.

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