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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