Error estimates for a finite element approximation of a minimal surface

Abstract:

A finite element approximation of the minimal surface problem for a strictly convex bounded plane domain $\Omega$ is considered. The approximating functions are continuous and piecewise linear on a triangulation of $\Omega$. Error estimates of the form $O(h)$ in the ${H^1}$ norm and $O({h^2})$ in the ${L_p}$-norm $(p < 2)$ are proved, where h denotes the maximal side in the triangulation.