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Surface finite element approximation of spherical Whittle-Matérn Gaussian random fields. (English) Zbl 07511041

Summary: Spherical Whittle-Matérn 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.

MSC:

65-XX Numerical analysis
35R60 PDEs with randomness, stochastic partial differential equations
60G60 Random fields
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
58J05 Elliptic equations on manifolds, general theory
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
65C30 Numerical solutions to stochastic differential and integral equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

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References:

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