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Convergent discrete Laplace-Beltrami operators over surfaces

Research paper by Jyh-Yang Wu, Mei-Hsiu Chi, Sheng-Gwo Chen

Indexed on: 20 Apr '10Published on: 20 Apr '10Published in: Computer Science - Computational Geometry



Abstract

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.