Discrete schemes for Gaussian curvature and their convergence

In this paper, several discrete schemes for Gaussian curvature are surveyed. The convergence property of a modified discrete scheme for the Gaussian curvature is proved. Furthermore, a new discrete scheme for Gaussian curvature is proposed. We show that this new scheme converges at the regular vertex with valence not less than 5. By constructing a counterexample, we also show that it is impossible for building a discrete scheme for Gaussian curvature which converges over the regular vertex with valence 4. Finally, asymptotic errors of several discrete schemes for Gaussian curvature are compared. AMS Subject Classifications: Primary 68U07, 68U05, 65S05, 53A40.

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Zhiqiang Xu, Guoliang Xu
• Keywords: CORR 2008, Discrete Schemes, Education, Gaussian Curvature, Modified Discrete Scheme