Solution of a Class of Minimal Surface Problem with Obstacle

Plateau’s problem is to determine the surface with minimal area that lies above an obstacle with given boundaryconditions. In this paper, a special example of this class of the problem is given and solved with the linearfinite element method. First, we triangulate the domain of definition, and transform the linear finite elementapproximation into a constrained nonlinear optimization problem. Then we introduce a simple and efficientmethod, named sequential quadratic programming, for solving the constrained nonlinear optimization problem.The sequential quadratic programming is implemented by the fmincon function in the optimization toolbox ofMATLAB. Also, we discuss the relations between the number of grids and the computing time as well as theprecision of the result.