528	RWTH Publication No: 849259        2022
TITLE	Diffusion of tangential tensor fields: numerical issues and influence of geometric properties
AUTHORS	Elena Bachini, Philip Brandner, Thomas Jankuhn, Michael Nestler, Simon Praetorius, Arnold Reusken, Axel Voigt
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.
KEYWORDS	finite elements, surface heat equation, tangential tensor fields
DOI	10.1515/jnma-2022-0088