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On the approximation of unstable parametric minimal surfaces |
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| Authors: | Gerhard Dziuk John E. Hutchinson |
| Affiliation: | (1) Institut für Angewandte Mathematik, Universität Freiburg, Hermann-Herder-Str. 10, D-79104 Freiburg i.Br., Germany;(2) Department of Mathematics, School of Mathematical Sciences, Australian National University, GPO Box 4, 0200 Canberra, ACT, Australia |
| Abstract: | We prove optimal convergence results for discrete approximations to (possibly unstable) minimal surfaces. This appears to be the first class of results of this type for geometric objects solving a highly non-linear geometric variational problem. We introduce a number of new techniques which we expect will be of use in other geometric problems. The theoretical approximation results are confirmed by numerical test computations. |
| Keywords: | 65N15 49Q05 65N30 53A10 65N38 |
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