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

02/17/2023

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by   Hiroki Ishizaka, et al.

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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.