Abstract
The cotangent formula constitutes an intrinsic discretization of the Laplace-Beltrami operator on polyhedral surfaces in a finite-element sense. This note gives an overview of approximation and convergence properties of discrete Laplacians and mean curvature vectors for polyhedral surfaces located in the vicinity of a smooth surface in euclidean 3-space. In particular, we show that mean curvature vectors converge in the sense of distributions, but fail to converge in L 2.
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Wardetzky, M. (2008). Convergence of the Cotangent Formula: An Overview. In: Bobenko, A.I., Sullivan, J.M., Schröder, P., Ziegler, G.M. (eds) Discrete Differential Geometry. Oberwolfach Seminars, vol 38. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8621-4_15
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DOI: https://doi.org/10.1007/978-3-7643-8621-4_15
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