Convergent discrete Laplace-Beltrami operators over surfaces

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. Key words: Local tangential polygon; discrete Laplace-Beltrami operators; Configuration Equation

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Jyh-Yang Wu, Mei-Hsiu Chi, Sheng-Gwo Chen
• Keywords: Convergence, CORR 2010, Discrete Laplace-beltrami Operators, Education, Laplace-Beltrami Operators