Two families of C1-Pk Fraeijs de Veubeke-Sander finite elements on quadrilateral meshes
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913848137613312 |
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| author | Zhang, Shangyou |
| author_facet | Zhang, Shangyou |
| contents | We extend the $C^1$-$P_3$ Fraeijs de Veubeke-Sander finite element to
two families of $C^1$-$P_k$ ($k>3$) macro finite elements on
general quadrilateral meshes. On each quadrilateral, four $P_k$ polynomials are defined on
the four triangles subdivided from the quadrilateral by
its two diagonal lines. The first family of $C^1$-$P_k$ finite elements is the full $C^1$-$P_k$
space on the macro-mesh. Thus the element can be applied to interface problems. The second family of $C^1$-$P_k$ finite elements condenses
all internal degrees of freedom by moving them to the four edges. Thus the second element method has much less unknowns but is
more accurate than the first one. We prove the uni-solvency and the optimal order convergence. Numerical tests and comparisons with the $C^1$-$P_k$ Argyris are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13968 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two families of C1-Pk Fraeijs de Veubeke-Sander finite elements on quadrilateral meshes Zhang, Shangyou Numerical Analysis 65N15, 65N30 We extend the $C^1$-$P_3$ Fraeijs de Veubeke-Sander finite element to two families of $C^1$-$P_k$ ($k>3$) macro finite elements on general quadrilateral meshes. On each quadrilateral, four $P_k$ polynomials are defined on the four triangles subdivided from the quadrilateral by its two diagonal lines. The first family of $C^1$-$P_k$ finite elements is the full $C^1$-$P_k$ space on the macro-mesh. Thus the element can be applied to interface problems. The second family of $C^1$-$P_k$ finite elements condenses all internal degrees of freedom by moving them to the four edges. Thus the second element method has much less unknowns but is more accurate than the first one. We prove the uni-solvency and the optimal order convergence. Numerical tests and comparisons with the $C^1$-$P_k$ Argyris are provided. |
| title | Two families of C1-Pk Fraeijs de Veubeke-Sander finite elements on quadrilateral meshes |
| topic | Numerical Analysis 65N15, 65N30 |
| url | https://arxiv.org/abs/2505.13968 |