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.

翻译：我们研究了曲面上切向张量值数据的扩散问题。为此，收集并使用了多种基于有限元的数值方法来求解曲面上的n阶切向张量热流问题。这些方法在曲面表示方式、所需几何信息以及切向条件的处理方法上有所不同。我们强调了几何性质的重要性，并指出随着张量阶数从n=0增加到n≥1，其影响逐渐增强。文中通过一个具体示例展示了曲率如何显著改变解的性态。