Our aim is to compute surfaces of the topological type of the disc
that are stationary points of the area functional. Since such
computations may be very time consuming, we derive an a posteriori
controlled adaptive algorithm based on a recently developed and
analyzed finite element method by Dziuk and Hutchinson.
For the implementation of the adaptive solver we use the adaptive
finite element toolbox ALBERT. Numerical results are
presented for the Enneper surface and a minimal surface with boundary
on a torus.

This is a joint work with Willy Doerfler, Universitaet Karlsruhe.