Surface finite element approximation of spherical Whittle--Matérn Gaussian random fields

Abstract: 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.