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Variational Methods for Discrete Geometric Functionals

In: Handbook of Variational Methods for Nonlinear Geometric Data

Author

Listed:
  • Henrik Schumacher

    (Institute for Mathematics, RWTH Aachen University)

  • Max Wardetzky

    (University of Göttingen, Institute of Numerical and Applied Mathematics)

Abstract

While consistent discrete notions of curvatures and differential operators have been widely studied, the question of whether the resulting minimizers converge to their smooth counterparts still remains open for various geometric functionals. Building on tools from variational analysis, and in particular using the notion of Kuratowski convergence, we offer a general framework for treating convergence of minimizers of (discrete) geometric functionals. We show how to apply the resulting machinery to minimal surfaces and Euler elasticae.

Suggested Citation

  • Henrik Schumacher & Max Wardetzky, 2020. "Variational Methods for Discrete Geometric Functionals," Springer Books, in: Philipp Grohs & Martin Holler & Andreas Weinmann (ed.), Handbook of Variational Methods for Nonlinear Geometric Data, chapter 0, pages 153-172, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-31351-7_5
    DOI: 10.1007/978-3-030-31351-7_5
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