• DOI:10.48550/arXiv.2205.12581
• Corpus ID: 249062988

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

@article{Bachini2022DiffusionOT,
  title={Diffusion of tangential tensor fields: numerical issues and influence of geometric properties},
  author={Elena Bachini and Philip Brandner and Thomas Jankuhn and Michael Nestler and Simon Praetorius and Arnold Reusken and Axel Voigt},
  journal={ArXiv},
  year={2022},
  volume={abs/2205.12581}
}

• Elena Bachini, Philip Brandner, +4 authors A. Voigt
• Published 25 May 2022
• Materials Science
• ArXiv

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.