Weak convergence of Galerkin approximations for fractional elliptic stochastic PDEs with spatial white noise
Artikel i vetenskaplig tidskrift, 2018

The numerical approximation of the solution to a stochastic partial differential equation with additive spatial white noise on a bounded domain is considered. The differential operator is assumed to be a fractional power of an integer order elliptic differential operator. The solution is approximated by means of a finite element discretization in space and a quadrature approximation of an integral representation of the fractional inverse from the Dunford–Taylor calculus. For the resulting approximation, a concise analysis of the weak error is performed. Specifically, for the class of twice continuously Fréchet differentiable functionals with second derivatives of polynomial growth, an explicit rate of weak convergence is derived, and it is shown that the component of the convergence rate stemming from the stochasticity is doubled compared to the corresponding strong rate. Numerical experiments for different functionals validate the theoretical results.

Matérn covariances

Finite element methods

Galerkin methods

Spatial statistics

Fractional operators

Stochastic partial differential equations

Weak convergence

Gaussian white noise

Författare

David Bolin

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Kristin Kirchner

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Mihaly Kovacs

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

BIT (Copenhagen)

0006-3835 (ISSN)

Vol. 58 4 881-906

Latenta hoppfält för spatial statistik

Vetenskapsrådet (VR), 2017-01-01 -- 2020-12-31.

Ämneskategorier

Beräkningsmatematik

Sannolikhetsteori och statistik

Matematisk analys

DOI

10.1007/s10543-018-0719-8

Mer information

Senast uppdaterat

2018-12-19