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

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

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

OriginalspracheEnglisch
Seitenumfang28
FachzeitschriftJournal of Numerical Mathematics
Frühes Online-Datum16 Aug. 2023
PublikationsstatusElektronische Veröffentlichung vor Drucklegung - 16 Aug. 2023
Peer-Review-StatusJa

Externe IDs

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

Schlagworte

DFG-Fachsystematik nach Fachkollegium

Fächergruppen, Lehr- und Forschungsbereiche, Fachgebiete nach Destatis

Schlagwörter

  • math.NA, cs.NA, 58J65, 65M22, 35R01, G.1.8, tangential tensor fields, surface heat equation, finite elements