Error estimates for a finite element approximation of a minimal surface
Claes Johnson, Vidar Thomée · Mathematics of Computation · 1975
A finite element approximation of the minimal surface problem for a strictly convex bounded plane domain Ω \Omega is considered. The approximating functions are continuous and piecewise linear on a triangulation of Ω \Omega . Error estimates of the form O ( h ) O(h) in the H 1 {H^1} norm and O ( h 2 ) O({h^2}) in the L p {L_p} -norm ( p > 2 ) (p > 2) are proved, where h denotes the maximal side in the triangulation.