Using Raviart-Thomas elements on a surface mesh

Hey y’all!

As a part of my master thesis, I’m trying to implement a mixed finite element method for a diffusion equation on a curved surface. This means that I have to use RT0 finite elements on a meshS. The problem is that functions in such a finite element space only have two components (e.g. [v1, v2]), whereas the global x-y-z coordinate system is obviously three-dimensional. In particular, this means that I can’t simply use dx,dy,dz to compute the surface divergence of such a function. How would I go about using RT0 elements on a meshS, and is it possible to compute the surface divergence?

Thanks in advance for your time!