Variational Methods for Discrete Geometric Functionals

Henrik Schumacher () and Max Wardetzky ()
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Henrik Schumacher: Institute for Mathematics, RWTH Aachen University
Max Wardetzky: University of Göttingen, Institute of Numerical and Applied Mathematics

Chapter Chapter 5 in Handbook of Variational Methods for Nonlinear Geometric Data, 2020, pp 153-172 from Springer

Abstract: 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.

Date: 2020
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DOI: 10.1007/978-3-030-31351-7_5

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