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 -

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.