We consider a finite element method for Partial Differential Equations (PDEs) on surfaces. Unlike many previous techniques, this approach is based on a geometrically intrinsic formulation. With proper definition of the geometry and transport operators, the resulting finite element method is fully intrinsic to the surface. Here, we lay out in detail the formulation and compare it to a well-established finite element scheme for surface PDEs. We then evaluate the method for several steady and transient problems involving both diffusion and advection-dominated regimes. The results show expected convergence rates and good performance relative to established finite element methods.

我们考虑表面上偏微分方程（PDE）的有限元方法。与许多以前的技术不同，此方法基于几何固有公式。正确定义几何形状和传输算符后，所得的有限元方法完全是曲面固有的。在这里，我们详细介绍了该公式，并将其与针对表面PDE的公认的有限元方案进行比较。然后，我们针对涉及扩散和对流占主导地位的几个稳态和瞬态问题评估该方法。结果表明相对于已建立的有限元方法，预期的收敛速度和良好的性能。