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Discrete schemes for Gaussian curvature and their convergence

Abstract

In this paper, several discrete schemes for Gaussian curvature are surveyed. The convergence property of a modified discrete scheme for the Gaussian curvature is considered. Furthermore, a new discrete scheme for Gaussian curvature is resented. We prove that the 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 scheme for Gaussian curvature are compared

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