Morley finite element analysis for fourth-order elliptic equations under a semi-regular mesh condition
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914921042673664 |
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| author | Ishizaka, Hiroki |
| author_facet | Ishizaka, Hiroki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_08719 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Morley finite element analysis for fourth-order elliptic equations under a semi-regular mesh condition Ishizaka, Hiroki Numerical Analysis 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. |
| title | Morley finite element analysis for fourth-order elliptic equations under a semi-regular mesh condition |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2302.08719 |