Abstract:We demonstrate that we can carry over the strategy of Finite Element Exterior Calculus (FEEC) to Summation-by-Parts (SBP) Finite Difference (FD) methods to achieve divergence- and curl-free discretizations. This is not obvious at first sight, as for SBP-FD no basis functions are known, but only values and derivatives at points. The key is a remarkable analytic relationship that enables us to construct compatible operators using integral and nodal degrees of freedom. Pre-existing SBP-FD matrix operators can then be used to obtain nodal values from the integral degrees of freedom to derive a scheme with the desired properties.
| Comments: | 50 pages, 18 figures, 14 tables |
| Subjects: | Numerical Analysis (math.NA) |
| MSC classes: | 65M06, 65M20 |
| Cite as: | arXiv:2511.20529 [math.NA] |
| (or arXiv:2511.20529v3 [math.NA] for this version) | |
| https://doi.org/10.48550/arXiv.2511.20529 arXiv-issued DOI via DataCite |
From: Daniel Bach [view email]
[v1]
Tue, 25 Nov 2025 17:34:30 UTC (2,275 KB)
[v2]
Wed, 26 Nov 2025 14:52:47 UTC (2,275 KB)
[v3]
Tue, 26 May 2026 16:39:39 UTC (2,230 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。