Intrinsic finite element method for advection-diffusion-reaction equations on surfaces

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.