Applications of Mathematics, Vol. 69, No. 6, pp. 769-805, 2024
Morley finite element analysis for fourth-order elliptic equations under a semi-regular mesh condition
Hiroki Ishizaka
Received May 5, 2024. Published online October 21, 2024.
Abstract: 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.
Keywords: Morley finite element; anisotropic interpolation error; fourth-order elliptic problem
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