Diffusion of tangential tensor fields: numerical issues and influence of geometric properties
Research output: Contribution to journal › Research article › Contributed › peer-review
Contributors
Abstract
We study the diffusion of tangential tensor-valued data on curved surfaces. For this purpose, several finite-element-based numerical methods are collected and used to solve a tangential surface n-tensor heat flow problem. These methods differ with respect to the surface representation used, the geometric information required, and the treatment of the tangentiality condition. We emphasize the importance of geometric properties and their increasing influence as the tensorial degree changes from n = 0 to n ≥ 1. A specific example is presented that illustrates how curvature drastically affects the behavior of the solution.
Details
Original language | English |
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Pages (from-to) | 55-75 |
Number of pages | 21 |
Journal | Journal of Numerical Mathematics |
Volume | 32 |
Issue number | 1 |
Early online date | 16 Aug 2023 |
Publication status | Published - 1 Mar 2024 |
Peer-reviewed | Yes |
External IDs
Scopus | 85168850529 |
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ORCID | /0000-0001-8610-9426/work/142248528 |
Keywords
DFG Classification of Subject Areas according to Review Boards
Subject groups, research areas, subject areas according to Destatis
ASJC Scopus subject areas
Keywords
- math.NA, cs.NA, 58J65, 65M22, 35R01, G.1.8, tangential tensor fields, surface heat equation, finite elements