Michael Hinze:

Zur numerischen Behandlung des Marx-Shiffmanschen Randwertproblems

Marx and Shiffman generalized Courants approach to the characterization of polygonal minimal surfaces presented in "Dirichlet's Integral and the Calculus of Variations". For this purpose they introduced quasiminimal surfaces which differ from Courant's minimal vectors in their boundary conditions. In this way Courant's function is generalized to a real-analytic function, as was proved by Heinz. As a consequence, polygonal minimal surfaces can be characterized with the help of the 2nd derivative of this new function. Here, the numerical frame for this approach is prepared. In particular a linear finite element method for the approximation of quasiminimal surfaces in the p-dimensional Euclidean space is investigated. Error estimates for the numerical approximation in terms of the angles of the bounding polygon are proven. Several examples of computed quasiminimal surfaces are presented.

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