A TraceFEM $C^0$ Interior Penalty Method for the Surface Biharmonic Equation
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908727366385664 |
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| author | Neilan, Michael Wan, Hongzhi |
| author_facet | Neilan, Michael Wan, Hongzhi |
| contents | We construct and analyze a TraceFEM discretization for the surface biharmonic problem. The method utilizes standard quadratic Lagrange finite element spaces defined on a three-dimensional background mesh and a symmetric $C^0$ interior penalty formulation posed on a second-order polyhedral approximation of the surface. Stability is achieved through a combination of surface edge penalties and bulk-facet penalization of gradient and Hessian jumps. We prove optimal first-order convergence in a discrete $H^2$ norm and quadratic convergence in the $L^2$ norm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18949 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A TraceFEM $C^0$ Interior Penalty Method for the Surface Biharmonic Equation Neilan, Michael Wan, Hongzhi Numerical Analysis 65N30 We construct and analyze a TraceFEM discretization for the surface biharmonic problem. The method utilizes standard quadratic Lagrange finite element spaces defined on a three-dimensional background mesh and a symmetric $C^0$ interior penalty formulation posed on a second-order polyhedral approximation of the surface. Stability is achieved through a combination of surface edge penalties and bulk-facet penalization of gradient and Hessian jumps. We prove optimal first-order convergence in a discrete $H^2$ norm and quadratic convergence in the $L^2$ norm. |
| title | A TraceFEM $C^0$ Interior Penalty Method for the Surface Biharmonic Equation |
| topic | Numerical Analysis 65N30 |
| url | https://arxiv.org/abs/2512.18949 |