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

翻译：我们考虑封闭表面的光谱分数拉普莱-贝特拉米问题的数字近似值。提议的数字算法依赖于其 Balakrishnan 集成表示法,它包括一个正弦二次方形,加上参数表面的标准限值元素方法。可能到一个日志期,当精确溶剂与其数字近似值之间的差异以2美元和1美元衡量时,观察到并分析得出最佳趋同率。算法的性能在不同的环境(包括表面高斯田的近似值)中作了说明。