Diffusion of tangential tensor fields: numerical issues and influence of geometric properties

Research output: Contribution to journalResearch articleContributedpeer-review



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.


Original languageEnglish
Number of pages28
JournalJournal of Numerical Mathematics
Early online date16 Aug 2023
Publication statusE-pub ahead of print - 16 Aug 2023

External IDs

Scopus 85168850529
ORCID /0000-0001-8610-9426/work/142248528


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