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

2021/01/13 by Andrea Bonito, Wenyu Lei, Bonito, Andrea +1 · 1 citation
Mathematics · #Numerical methods in inverse problems #Approximation Theory and Sequence Spaces #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2101.05141

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 L² and H¹. The performances of the algorithms are illustrated in different settings including the approximation of Gaussian fields on surfaces.

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