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Article Dans Une Revue IMA Journal of Numerical Analysis Année : 2017

Approximation of the invariant law of SPDEs: error analysis using a Poisson equation for a full-discretization scheme

Résumé

We study the long-time behavior of fully discretized semilinear SPDEs with additive space-time white noise, which admit a unique invariant probability measure $\mu$. We show that the average of regular enough test functions with respect to the (possibly non unique) invariant laws of the approximations are close to the corresponding quantity for $\mu$. More precisely, we analyze the rate of the convergence with respect to the different discretization parameters. Here we focus on the discretization in time thanks to a scheme of Euler type, and on a Finite Element discretization in space. The results rely on the use of a Poisson equation; we obtain that the rates of convergence for the invariant laws are given by the weak order of the discretization on finite time intervals: order $1/2$ with respect to the time-step and order $1$ with respect to the mesh-size.
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Dates et versions

hal-00910323 , version 1 (28-11-2013)
hal-00910323 , version 2 (16-02-2014)

Identifiants

Citer

Charles-Edouard Bréhier, Marie Kopec. Approximation of the invariant law of SPDEs: error analysis using a Poisson equation for a full-discretization scheme. IMA Journal of Numerical Analysis, 2017, 37 (3), pp.1. ⟨10.1093/imanum/drw030⟩. ⟨hal-00910323v2⟩
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