An FDM-sFEM scheme on time-space manifolds and its superconvergence analysis
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866918102693838848 |
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| author | Jiang, Chengrun Dong, Guozhi Guo, Hailong Shi, Zuoqiang |
| author_facet | Jiang, Chengrun Dong, Guozhi Guo, Hailong Shi, Zuoqiang |
| contents | We study superconvergent discretization of the Laplace-Beltrami operator on time-space product manifolds with Neumann temporal boundary values, which arise in the context of dynamic optimal transport on general surfaces. We propose a coupled scheme that combines finite difference methods in time with surface finite element methods in space. By establishing a new summation by parts formula and proving the supercloseness of the semi-discrete solution, we derive superconvergence results for the recovered gradient via post-processing techniques. In addition, our geometric error analysis is implemented within a novel framework based on the approximation of the Riemannian metric. Several numerical examples are provided to validate and illustrate the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17378 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An FDM-sFEM scheme on time-space manifolds and its superconvergence analysis Jiang, Chengrun Dong, Guozhi Guo, Hailong Shi, Zuoqiang Numerical Analysis 65M15, 65M60 We study superconvergent discretization of the Laplace-Beltrami operator on time-space product manifolds with Neumann temporal boundary values, which arise in the context of dynamic optimal transport on general surfaces. We propose a coupled scheme that combines finite difference methods in time with surface finite element methods in space. By establishing a new summation by parts formula and proving the supercloseness of the semi-discrete solution, we derive superconvergence results for the recovered gradient via post-processing techniques. In addition, our geometric error analysis is implemented within a novel framework based on the approximation of the Riemannian metric. Several numerical examples are provided to validate and illustrate the theoretical results. |
| title | An FDM-sFEM scheme on time-space manifolds and its superconvergence analysis |
| topic | Numerical Analysis 65M15, 65M60 |
| url | https://arxiv.org/abs/2507.17378 |