TY - JOUR
T1 - Approximation of the Spectral Fractional Powers of the Laplace-Beltrami Operator
AU - Bonito , Andrea
AU - Lei , Wenyu
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 1193
EP - 1218
PY - 2022
DA - 2022/10
SN - 15
DO - http://doi.org/10.4208/nmtma.OA-2022-0005s
UR - https://global-sci.org/intro/article_detail/nmtma/21099.html
KW - Fractional diffusion, Laplace-Beltrami, FEM parametric methods on surfaces, Gaussian fields.
AB - <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>