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.
|Number of pages||28|
|Journal||Journal of Numerical Mathematics|
|Early online date||16 Aug 2023|
|Publication status||E-pub ahead of print - 16 Aug 2023|
DFG Classification of Subject Areas according to Review Boards
Subject groups, research areas, subject areas according to Destatis
- math.NA, cs.NA, 58J65, 65M22, 35R01, G.1.8, tangential tensor fields, surface heat equation, finite elements