Convergent discrete Laplace-Beltrami operators over surfaces

Details Convergent discrete Laplace-Beltrami operators over surfaces Convergent discrete Laplace-Beltrami operators over surfaces

2010-04-20

arxiv.org/abs/1004.3486v1

Computer Science

Computational Geometry

13 pages and 4 figures

Scientific paper

The convergence problem of the Laplace-Beltrami operators plays an essential role in the convergence analysis of the numerical simulations of some important geometric partial differential equations which involve the operator. In this note we present a new effective and convergent algorithm to compute discrete Laplace-Beltrami operators acting on functions over surfaces. We prove a convergence theorem for our discretization. To our knowledge, this is the first convergent algorithm of discrete Laplace-Beltrami operators over surfaces for functions on general surfaces. Our algorithm is conceptually simple and easy to compute. Indeed, the convergence rate of our new algorithm of discrete Laplace-Beltrami operators over surfaces is $O(r)$ where r represents the size of the mesh of discretization of the surface.

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