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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.21821 |
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| _version_ | 1866918403524001792 |
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| author | Grošelj, Jan Praprotnik, Ada Šadl Speleers, Hendrik |
| author_facet | Grošelj, Jan Praprotnik, Ada Šadl Speleers, Hendrik |
| contents | In this paper, we consider $C^1$ cubic Powell-Sabin splines for the numerical solution of boundary value problems on planar and spatial surface domains. We first review the construction and basic properties of polynomial and rational $C^1$ cubic Powell-Sabin spline representations on unstructured triangulations. Then, we discuss how these flexible representations can be exploited to create geometry mappings suited for a precise description of (classes of) surface domains. This is illustrated with several examples. Finally, the obtained domain descriptions are utilized in the isogeometric analysis framework for solving various Poisson and biharmonic problems. It is demonstrated that $C^1$ cubic Powell-Sabin splines form a powerful alternative to $C^0$ cubic Lagrange elements and bicubic NURBS. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21821 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Isogeometric analysis with $C^1$ cubic Powell-Sabin splines Grošelj, Jan Praprotnik, Ada Šadl Speleers, Hendrik Numerical Analysis In this paper, we consider $C^1$ cubic Powell-Sabin splines for the numerical solution of boundary value problems on planar and spatial surface domains. We first review the construction and basic properties of polynomial and rational $C^1$ cubic Powell-Sabin spline representations on unstructured triangulations. Then, we discuss how these flexible representations can be exploited to create geometry mappings suited for a precise description of (classes of) surface domains. This is illustrated with several examples. Finally, the obtained domain descriptions are utilized in the isogeometric analysis framework for solving various Poisson and biharmonic problems. It is demonstrated that $C^1$ cubic Powell-Sabin splines form a powerful alternative to $C^0$ cubic Lagrange elements and bicubic NURBS. |
| title | Isogeometric analysis with $C^1$ cubic Powell-Sabin splines |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2603.21821 |