Approximation of SPDE covariance operators by finite elements: a semigroup approach
Artikel i vetenskaplig tidskrift, 2023

The problem of approximating the covariance operator of the mild solution to a linear stochastic partial differential equation is considered. An integral equation involving the semigroup of the mild solution is derived and a general error decomposition is proven. This formula is applied to approximations of the covariance operator of a stochastic advection-diffusion equation and a stochastic wave equation, both on bounded domains. The approximations are based on finite element discretizations in space and rational approximations of the exponential function in time. Convergence rates are derived in the trace class and Hilbert-Schmidt norms with numerical simulations illustrating the results.

stochastic wave equations

covariance operators

finite element method

integral equations

stochastic advection-diffusion equations

stochastic partial differential equations

Författare

Mihaly Kovacs

Chalmers, Matematiska vetenskaper

Budapesti Muszaki es Gazdasagtudomanyi Egyetem

Pázmány Péter Katolikus Egyetem

Göteborgs universitet

Annika Lang

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Andreas Petersson

Universitetet i Oslo

IMA Journal of Numerical Analysis

0272-4979 (ISSN) 1464-3642 (eISSN)

Vol. 43 3 1324-1357

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Ämneskategorier

Beräkningsmatematik

Sannolikhetsteori och statistik

Matematisk analys

DOI

10.1093/imanum/drac020

Mer information

Senast uppdaterat

2023-07-05