Spherical Whittle--Mat\'ern Gaussian random fields are considered as solutions to fractional elliptic stochastic partial differential equations on the sphere. Approximation is done with surface finite elements. While the non-fractional part of the operator is solved by a recursive scheme, a quadrature of the Dunford--Taylor integral representation is employed for the fractional part. Strong error analysis is performed, and the computational complexity is bounded in terms of the accuracy. Numerical experiments for different choices of parameters confirm the theoretical findings.

翻译：球形Whittle-Mat\'ern Gaussian 随机字段被视为对球体上分数的椭圆形局部偏差方程式的解决方案。 接近于表面限制元素。 虽然操作员的非违规部分通过递归方案解决, 但对分数部分则采用Dunford- Taylor集成代表方块的二次方块。 进行了强烈的错误分析, 计算的复杂性在准确性上被捆绑。 对不同参数选择的数值实验证实了理论结论 。