@misc{HildebrandtPolthierWardetzky, author = {Hildebrandt, Klaus and Polthier, Konrad and Wardetzky, Max}, title = {On the Convergence of Metric and Geometric Properties of Polyhedral Surfaces}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8587}, number = {05-24}, abstract = {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.}, language = {en} }