@Article{NMTMA-15-1193,
author = {Bonito , Andrea and Lei , Wenyu},
title = {Approximation of the Spectral Fractional Powers of the Laplace-Beltrami Operator},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2022},
volume = {15},
number = {4},
pages = {1193--1218},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2022-0005s},
url = {http://global-sci.org/intro/article_detail/nmtma/21099.html}
}