I've been working on a new method for 2-dimensional FEM on Riemannian Manifolds that involves using geodesic Triangles instead of approximating them in an embedded form using "traditional" triangles.

I'm quite far along, and up until now I wasn't even sure if my Method would only work on an abstract level or if it can actually be applied. So far, it works for trivial cases ($\mathbb{R}^2, S^2$,...), which is "good enough" at this point.

Now my problem is this: I've been searching high and low (using Zentralblatt MATH) for any research related to mine in any way. So far, all I could find is a single paper (http://vs24.kobv.de/documents-matheon/580/6086_sander_geodesic_fe.pdf).

I find it hard to believe that nothing else exists on this matter.

My questions are:

- Does anyone know any research done in this direction?
- Or is the Idea "useless" (as in, it wouldn't improve the result)?
- Or have I simply been searching wrong?

Any feedback is appreciated