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 is observed and derived analytically when the discrepancies between the exact solution and its numerical approximations are measured in $L^2$ and $H^1$.

翻译：我们认为封闭表面的光谱分数拉普莱-贝特拉米问题的数字近似值。提议的数字算法以其Balakrishnan整体表示法为基础,并包含一个正弦之象,加上参数表面的标准有限元素方法。 可能到一个日志期,当精确解决方案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。