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.

中文翻译：

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切向张量场的扩散：数值问题和几何性质的影响

我们研究切向张量值数据在曲面上的扩散。为此，收集了几种基于有限元的数值方法并用于求解切向曲面n-张量热流问题。这些方法在使用的表面表示、所需的几何信息以及切向条件的处理方面有所不同。我们强调几何性质的重要性及其随着张量度从n= 0 至n≥ 1。给出了一个具体示例，说明曲率如何极大地影响解的行为。