The sharpness condition for constructing a finite element from a superspline
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915203919118336 |
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| author | Hu, Jun Lin, Ting Wu, Qingyu Yuan, Beihui |
| author_facet | Hu, Jun Lin, Ting Wu, Qingyu Yuan, Beihui |
| contents | This paper addresses sharpness conditions for constructing $C^r$ conforming finite element spaces from a superspline spaces on general simplicial triangulations. We introduce the concept of extendability for the pre-element spaces, which encompasses both the superspline spaces and the finite element spaces. By examining the extendability condition for both types of spaces, we provide an answer to the conditions regarding the construction. A corollary of our results is that constructing $C^r$ conforming elements in $d$ dimensions generally requires an extra $C^{2^{s}r}$ continuity on $s$-codimensional simplices, and the polynomial degree is at least $(2^d r + 1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03680 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The sharpness condition for constructing a finite element from a superspline Hu, Jun Lin, Ting Wu, Qingyu Yuan, Beihui Numerical Analysis 65N30, 65D07 This paper addresses sharpness conditions for constructing $C^r$ conforming finite element spaces from a superspline spaces on general simplicial triangulations. We introduce the concept of extendability for the pre-element spaces, which encompasses both the superspline spaces and the finite element spaces. By examining the extendability condition for both types of spaces, we provide an answer to the conditions regarding the construction. A corollary of our results is that constructing $C^r$ conforming elements in $d$ dimensions generally requires an extra $C^{2^{s}r}$ continuity on $s$-codimensional simplices, and the polynomial degree is at least $(2^d r + 1)$. |
| title | The sharpness condition for constructing a finite element from a superspline |
| topic | Numerical Analysis 65N30, 65D07 |
| url | https://arxiv.org/abs/2407.03680 |