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.
Funding statement: The authors wish to thank the German Research Foundation (DFG) for financial support within the Research Unit ‘Vector- and Tensor-Valued Surface PDEs’ (FOR 3013) with projects No. RE 1461/11-1 and VO 899/22-1. We further acknowledge computing resources provided by ZIH at TU Dresden and within project PFAMDIS at FZ Jülich.
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