Surface finite element approximation of spherical Whittle-Matérn Gaussian random fields
Journal article, 2021

Spherical Matérn-Whittle 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, obtaining polynomial convergence in the white noise approximation, exponential convergence in the quadrature, and quadratic convergence in the mesh width of the discretization of the sphere. Numerical experiments for different choices of parameters confirm the theoretical findings.

Gaussian random fields

Stochastic partial differential equations

Sphere

Surface finite element method

Parametric finite element methods

Strong convergence

Fractional operators

Author

Erik Jansson

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Mihaly Kovacs

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Annika Lang

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

SIAM Journal of Scientific Computing

1064-8275 (ISSN) 1095-7197 (eISSN)

Vol. 44 2 A825-A842

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Subject Categories

Computational Mathematics

Probability Theory and Statistics

Mathematical Analysis

Roots

Basic sciences

DOI

10.1137/21M1400717

More information

Latest update

5/17/2022