Convergence of the Cotangent Formula: An Overview

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 .