Rectangular $C^1$-$P_k$ finite elements with $Q_k$-bubble enrichment
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915673104449536 |
|---|---|
| author | Zhang, Shangyou |
| author_facet | Zhang, Shangyou |
| contents | We enrich the $P_k$ polynomial space by $5$ ($k=4$), or $7$ ($k=5$), or 8 (all $k\ge 6$) $Q_k$ bubble functions to obtain a family of $C^1$-$P_k$ ($k\ge 4$) finite elements on rectangular meshes. We show the uni-solvency, the $C^1$-continuity and the quasi-optimal convergence. Numerical tests on the new $C^1$-$P_k$, $k=4,5,6,7$ and $8$, elements are performed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12152 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rectangular $C^1$-$P_k$ finite elements with $Q_k$-bubble enrichment Zhang, Shangyou Numerical Analysis 65N15, 65N30 We enrich the $P_k$ polynomial space by $5$ ($k=4$), or $7$ ($k=5$), or 8 (all $k\ge 6$) $Q_k$ bubble functions to obtain a family of $C^1$-$P_k$ ($k\ge 4$) finite elements on rectangular meshes. We show the uni-solvency, the $C^1$-continuity and the quasi-optimal convergence. Numerical tests on the new $C^1$-$P_k$, $k=4,5,6,7$ and $8$, elements are performed. |
| title | Rectangular $C^1$-$P_k$ finite elements with $Q_k$-bubble enrichment |
| topic | Numerical Analysis 65N15, 65N30 |
| url | https://arxiv.org/abs/2512.12152 |