surface gradient of a Function

Question

Hello,
I would like to compute surface gradient of a function u over a surface mesh (e.g. spherical surface) embedded in 3D:
surface_grad = (nabla_grad(u) - dot(nabla_grad(u), n)*n) *ds
where n is a unit normal to the surface. Any helps are appreciated.
I am using FEniCS 1.3.0 C++ version.
Thanks!
Dang

Answer 1

You may want to check the article by Marie Rognes et al. which explains quite explicitly how to implement this in Fenics. If you want to derive the orientation from the mesh data (instead of prescriping an explicit normal field) see also this post.