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Numerische Mathematik

, Volume 141, Issue 1, pp 173–213 | Cite as

Variational convergence of discrete minimal surfaces

  • Henrik SchumacherEmail author
  • Max Wardetzky
Article
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Abstract

Building on and extending tools from variational analysis and relying on certain a priori assumptions, we prove Kuratowski convergence of sets of simplicial area minimizers to minimizers of the smooth Douglas–Plateau problem under simplicial refinement. This convergence is with respect to a topology that is finer than the topology of uniform convergence of both positions and surface normals.

Mathematics Subject Classification

49Q05 53A10 58E12 

Notes

Acknowledgements

The authors would like to thank Heiko von der Mosel for discussions on the regularity of minimal surfaces.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for MathematicsRWTH Aachen UniversityAachenGermany
  2. 2.Institute for Numerical and Applied MathematicsGeorg-August-University GöttingenGöttingenGermany

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