The Laplace-Beltrami operator, used in various PDEs such as the heat equation or the wave equation, has been discretized very early using discrete structures in order to approximate solutions of these PDEs. We focus here on its uses in geometry processing, where we use mathematicals tools and concepts in order to manipulate 3D discrete objects such as surface meshes, volume meshes or point clouds. In particular, we stufy the discretization of these operators on digital surfaces, which are surfaces that can be found when studying object in Z³, where existing standard methods do not converge. We propose new « corrected »methods (based on a corrected normal field provided by an estimator) and experimentally verify that the results obtained with these operators converge towards the expected results if the surface was smooth. We also look at the use of these operators in surface regularization. Finally, we discuss the problem of UV maps generation, and we propose new simultaneous optimization methods of the seams and the distorsion based on the Ambrosio-Tortorelli functional.