Approximation of the Spectral Fractional Powers of the Laplace-Beltrami Operator

Approximation of the Spectral Fractional Powers of the Laplace-Beltrami Operator

Year:    2022

Author:    Wenyu Lei, Andrea Bonito, Wenyu Lei

Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 4 : pp. 1193–1218

Abstract

We consider numerical approximation of spectral fractional Laplace-Beltrami problems on closed surfaces. The proposed numerical algorithms rely on their Balakrishnan integral representation and consists a sinc quadrature coupled with standard finite element methods for parametric surfaces. Possibly up to a log term, optimal rate 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 on different settings including the approximation of Gaussian fields on surfaces.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2022-0005s

Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 4 : pp. 1193–1218

Published online:    2022-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    26

Keywords:    Fractional diffusion Laplace-Beltrami FEM parametric methods on surfaces Gaussian fields.

Author Details

Wenyu Lei

Andrea Bonito

Wenyu Lei