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

Sphere

Fractional operators

Stochastic partial differential equations

Gaussian random fields

Strong convergence

Parametric finite element methods

Surface finite element method

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

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Subject Categories

Computational Mathematics

Probability Theory and Statistics

Mathematical Analysis

Roots

Basic sciences

Related datasets

arXiv preprint 2102.08822 [dataset]

URI: https://arxiv.org/abs/2102.08822

More information

Latest update

2/19/2021