Spline-based solution transfer for space-time methods in 2D+t
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913507680714752 |
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| author | Larose, Logan Anderson, Jude T. Williams, David M. |
| author_facet | Larose, Logan Anderson, Jude T. Williams, David M. |
| contents | This work introduces a new solution-transfer process for slab-based space-time finite element methods. The new transfer process is based on Hsieh-Clough-Tocher (HCT) splines and satisfies the following requirements: (i) it maintains high-order accuracy up to 4th order, (ii) it preserves a discrete maximum principle, (iii) it asymptotically enforces mass conservation, and (iv) it constructs a smooth, continuous surrogate solution in between space-time slabs. While many existing transfer methods meet the first three requirements, the fourth requirement is crucial for enabling visualization and boundary condition enforcement for space-time applications. In this paper, we derive an error bound for our HCT spline-based transfer process. Additionally, we conduct numerical experiments quantifying the conservative nature and order of accuracy of the transfer process. Lastly, we present a qualitative evaluation of the visualization properties of the smooth surrogate solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11639 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spline-based solution transfer for space-time methods in 2D+t Larose, Logan Anderson, Jude T. Williams, David M. Numerical Analysis This work introduces a new solution-transfer process for slab-based space-time finite element methods. The new transfer process is based on Hsieh-Clough-Tocher (HCT) splines and satisfies the following requirements: (i) it maintains high-order accuracy up to 4th order, (ii) it preserves a discrete maximum principle, (iii) it asymptotically enforces mass conservation, and (iv) it constructs a smooth, continuous surrogate solution in between space-time slabs. While many existing transfer methods meet the first three requirements, the fourth requirement is crucial for enabling visualization and boundary condition enforcement for space-time applications. In this paper, we derive an error bound for our HCT spline-based transfer process. Additionally, we conduct numerical experiments quantifying the conservative nature and order of accuracy of the transfer process. Lastly, we present a qualitative evaluation of the visualization properties of the smooth surrogate solution. |
| title | Spline-based solution transfer for space-time methods in 2D+t |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2409.11639 |