A flexible model for non-stationary Gaussian random fields on hypersurfaces is introduced.The class of random fields on curves and surfaces is characterized by an amplitude spectral density of a second order elliptic differential operator.Sampling is done by a Galerkin--Chebyshev approximation based on the surface finite element method and Chebyshev polynomials. Strong error bounds are shown with convergence rates depending on the smoothness of the approximated random field. Numerical experiments that confirm the convergence rates are presented.

翻译：本文引入了一种在超曲面上定义非平稳高斯随机场的灵活模型。该类在曲线与曲面上的随机场由二阶椭圆微分算子的振幅谱密度所表征。采样通过基于曲面有限元方法和切比雪夫多项式的伽辽金-切比雪夫逼近实现。文中证明了强误差界，其收敛速率取决于所逼近随机场的平滑度。数值实验验证了所展示的收敛速率。