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

  1. Numerical Approximation of Gaussian Random Fields on Closed Surfaces

    Bonito, Andrea

    Guignard, Diane

    Lei, Wenyu

    Computational Methods in Applied Mathematics, Vol. 24 (2024), Iss. 4 P.829

    https://doi.org/10.1515/cmam-2022-0237 [Citations: 2]