Minimal surface computation using a finite element method on an embedded   surface
  We suggest a finite element method for computing minimal surfaces based on computing a discrete Laplace-Beltrami operator operating on the coordinates of the surface. The surface is a discrete representation of the zero level set of a distance function using linear tetrahedral finite elements, and the finite element discretization is done on the piecewise planar isosurface using the shape functions from the background three dimensional mesh used to represent the distance function. A recently suggested stabilization scheme is a crucial component in the method. 
Mirza Cenanovic, Peter Hansbo, Mats G. Larson
math.NA