Article
| Title: | Morley finite element analysis for fourth-order elliptic equations under a semi-regular mesh condition (English) |
| Author: | Ishizaka, Hiroki |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 69 |
| Issue: | 6 |
| Year: | 2024 |
| Pages: | 769-805 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | 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. (English) |
| Keyword: | Morley finite element |
| Keyword: | anisotropic interpolation error |
| Keyword: | fourth-order elliptic problem |
| MSC: | 65D05 |
| MSC: | 65N30 |
| DOI: | 10.21136/AM.2024.0103-24 |
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| Date available: | 2024-12-13T19:00:07Z |
| Last updated: | 2024-12-16 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152669 |
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