We consider the numerical approximation of Gaussian random fields on closed surfaces defined as the solution to a fractional stochastic partial differential equation (SPDE) with additive white noise. The SPDE involves two parameters controlling the smoothness and the correlation length of the Gaussian random field. The proposed numerical method relies on the Balakrishnan integral representation of the solution and does not require the approximation of eigenpairs. Rather, it consists of a sinc quadrature coupled with a standard surface finite element method. We provide a complete error analysis of the method and illustrate its performances by several numerical experiments.

翻译：我们考虑闭曲面上高斯随机场的数值逼近问题，该随机场定义为带有加性白噪声的分数阶随机偏微分方程（SPDE）的解。该SPDE包含两个参数，分别控制高斯随机场的光滑性和相关长度。所提出的数值方法基于解的Balakrishnan积分表示，无需逼近特征对，而是采用sinc求积与标准曲面有限元方法相结合。我们给出了该方法的完整误差分析，并通过多个数值实验展示了其性能。