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| Plateau’s problem is to determine the surface with minimal area that lies above an obstacle with given boundary conditions. In this paper, a special example of this class of the problem is given and solved with the linear finite element method. First, we triangulate the domain of definition, and transform the linear finite element approximation into a constrained nonlinear optimization problem. Then we introduce a simple and efficient method, 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 of MATLAB. Also, we discuss the relations between the number of grids and the computing time as well as the precision of the result. |
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| Keywords:minimal surface problem with obstacle; finite element approximation; constrained nonlinear optimization; sequential quadratic programming |
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