Wagner [1] devised algorithms for the numerical solution of the minimal surface equation using a finite element method. Numerical solutions to a number of classical soap film problems were thus obtained. The method did not allow for cases where several films met in a single curve. This paper gives appropriate patchings in cases where these singular curves arise. Such phenomena are quite common in real problems, so the paper is genuinely relevant. A successive over-relaxation method is used to determine the surface: defined plausibly as the direction of movement on a singular curve.

A set of examples is then given which show the technique in action. In some cases, solutions are verified against an analytic solution. In addition, some practical hints on how to accelerate convergence are given. Finally, the model is applied to the problem of constructing artificial human heart valves, which gave rise to the interest in the first place. The paper is interesting reading and capable of being understood fairly easily. Some nice pictures are included and the application is significant.