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Weak convergence for a spatial approximation of the nonlinear stochastic heat equation

Adam Andersson (Institutionen för matematiska vetenskaper, matematik) ; Stig Larsson (Institutionen för matematiska vetenskaper, matematik)
Mathematics of Computation (0025-5718). Vol. 85 (2016), p. 1335-1358.
[Artikel, refereegranskad vetenskaplig]

We find the weak rate of convergence of the spatially semidiscrete finite element approximation of the nonlinear stochastic heat equation. Both multiplicative and additive noise is considered under different assumptions. This extends an earlier result of Debussche in which time discretization is considered for the stochastic heat equation perturbed by white noise. It is known that this equation has a solution only in one space dimension. In order to obtain results for higher dimensions, colored noise is considered here, besides white noise in one dimension. Integration by parts in the Malliavin sense is used in the proof. The rate of weak convergence is, as expected, essentially twice the rate of strong convergence.

Nyckelord: Nonlinear stochastic heat equation, SPDE, finite element, error estimate, weak convergence, multiplicative noise, Malliavin calculus



Denna post skapades 2015-10-29. Senast ändrad 2016-11-03.
CPL Pubid: 225028

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Numerisk analys
Matematisk statistik

Chalmers infrastruktur