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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.00338 |
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| _version_ | 1866911898620919808 |
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| author | Ainsworth, Mark Parker, Charles |
| author_facet | Ainsworth, Mark Parker, Charles |
| contents | We develop a method to compute $H^2$-conforming finite element approximations in both two and three space dimensions using readily available finite element spaces. This is accomplished by deriving a novel, equivalent mixed variational formulation involving spaces with at most $H^1$-smoothness, so that conforming discretizations require at most $C^0$-continuity. The method is demonstrated on arbitrary order $C^1$-splines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00338 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two and three dimensional $H^2$-conforming finite element approximations without $C^1$-elements Ainsworth, Mark Parker, Charles Numerical Analysis 65N30 65N12 We develop a method to compute $H^2$-conforming finite element approximations in both two and three space dimensions using readily available finite element spaces. This is accomplished by deriving a novel, equivalent mixed variational formulation involving spaces with at most $H^1$-smoothness, so that conforming discretizations require at most $C^0$-continuity. The method is demonstrated on arbitrary order $C^1$-splines. |
| title | Two and three dimensional $H^2$-conforming finite element approximations without $C^1$-elements |
| topic | Numerical Analysis 65N30 65N12 |
| url | https://arxiv.org/abs/2406.00338 |