Approximation of the spectral fractional powers of the Laplace-Beltrami Operator

Andrea Bonito; Wenyu Lei

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arXiv · 2101.05141

Approximation of the spectral fractional powers of the Laplace-Beltrami Operator

Andrea Bonito·Wenyu Lei

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Abstract

We consider numerical approximations of spectral fractional Laplace-Beltrami problems on closed surfaces. The proposed numerical algorithms rely on their Balakrishnan integral representation and consist of a sinc quadrature coupled with standard finite element methods for parametric surfaces. Possibly up to a log term, optimal rates of convergence are observed and derived analytically when the discrepancies between the exact solution and its numerical approximations are measured in $L^2$ and $H^1$. The performances of the algorithms are illustrated in different settings including the approximation of Gaussian fields on surfaces.

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Andrea Bonito, Wenyu Lei. 2021-01-13. Approximation of the spectral fractional powers of the Laplace-Beltrami Operator. https://arxiv.org/abs/2101.05141

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