Geodesic
Morley finite element analysis for fourth-order elliptic equations under a semi-regular mesh condition
Applications of Mathematics, Tome 69 (2024) no. 6, pp. 769-805 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/AM.2024.0103-24
Classification : 65D05, 65N30
Keywords: Morley finite element; anisotropic interpolation error; fourth-order elliptic problem 
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Ishizaka, Hiroki. Morley finite element analysis for fourth-order elliptic equations under a semi-regular mesh condition. Applications of Mathematics, Tome 69 (2024) no. 6, pp. 769-805. doi: 10.21136/AM.2024.0103-24

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