Rectangular $C^1$-$Q_k$ Bell finite elements in two and three dimensions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913919326486528 |
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| author | Hu, Hongling Zhang, Shangyou |
| author_facet | Hu, Hongling Zhang, Shangyou |
| contents | Both the function and its normal derivative on the element boundary are $Q_k$ polynomials
for the Bogner-Fox-Schmit $C^1$-$Q_k$ finite element functions. Mathematically, to keep the optimal order of approximation, their spaces are required to
include $P_k$ and $P_{k-1}$ polynomials respectively. We construct a Bell type $C^1$-$Q_k$ finite element on rectangular meshes in 2D and 3D,
which has its normal derivative as a $Q_{k-1}$ polynomial on each face, for $k\ge 4$. We show, with a big reduction of the space, the $C^1$-$Q_k$ Bell
finite element retains the optimal order of convergence. Numerical experiments are performed, comparing the new elements with the original elements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23702 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rectangular $C^1$-$Q_k$ Bell finite elements in two and three dimensions Hu, Hongling Zhang, Shangyou Numerical Analysis Both the function and its normal derivative on the element boundary are $Q_k$ polynomials for the Bogner-Fox-Schmit $C^1$-$Q_k$ finite element functions. Mathematically, to keep the optimal order of approximation, their spaces are required to include $P_k$ and $P_{k-1}$ polynomials respectively. We construct a Bell type $C^1$-$Q_k$ finite element on rectangular meshes in 2D and 3D, which has its normal derivative as a $Q_{k-1}$ polynomial on each face, for $k\ge 4$. We show, with a big reduction of the space, the $C^1$-$Q_k$ Bell finite element retains the optimal order of convergence. Numerical experiments are performed, comparing the new elements with the original elements. |
| title | Rectangular $C^1$-$Q_k$ Bell finite elements in two and three dimensions |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2506.23702 |