TY - GEN A1 - Hildebrandt, Klaus A1 - Polthier, Konrad A1 - Wardetzky, Max T1 - On the Convergence of Metric and Geometric Properties of Polyhedral Surfaces N2 - We provide conditions for convergence of polyhedral surfaces and their discrete geometric properties to smooth surfaces embedded in Euclidian $3$-space. The notion of totally normal convergence is shown to be equivalent to the convergence of either one of the following: surface area, intrinsic metric, and Laplace-Beltrami operators. We further s how that totally normal convergence implies convergence results for shortest geodesics, mean curvature, and solutions to the Dirichlet problem. This work provides the justification for a discrete theory of differential geometric operators defined on polyhedral surfaces based on a variational formulation. T3 - ZIB-Report - 05-24 KW - Discrete Geometry KW - Differential Geometry KW - Numerical Analysis Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8587 ER -