SURFACE FINITE ELEMENT APPROXIMATION OF SPHERICAL WHITTLE--MAT\'ERN GAUSSIAN RANDOM FIELDS

Spherical Whittle--Mate'\rn 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 nonfractional 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.

Automated summary

This paper considers the solution of fractional elliptic stochastic partial differential equations on the sphere using Spherical Whittle--Mate'\rn Gaussian random fields. The approximation is done using surface finite elements and a quadrature of the Dunford-Taylor integral representation. Strong error analysis is performed and the computational complexity is bounded. Numerical experiments confirm the theoretical findings.