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Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise

Mihaly Kovacs ; Stig Larsson (Institutionen för matematiska vetenskaper, matematik) ; Fredrik Lindgren (Institutionen för matematiska vetenskaper, matematik)
BIT Numerical Mathematics (0006-3835). Vol. 52 (2012), 1, p. 85-108.
[Artikel, refereegranskad vetenskaplig]

A unified approach is given for the analysis of the weak error of spatially semidiscrete finite element methods for linear stochastic partial differential equations driven by additive noise. An error representation formula is found in an abstract setting based on the semigroup formulation of stochastic evolution equations. This is then applied to the stochastic heat, linearized Cahn-Hilliard, and wave equations. In all cases it is found that the rate of weak convergence is twice the rate of strong convergence, sometimes up to a logarithmic factor, under the same or, essentially the same, regularity requirements.

Nyckelord: Finite element, Parabolic equation, Hyperbolic equation, Stochastic, Heat equation, Cahn-Hilliard-Cook equation, Wave equation, Additive noise, Wiener process, Error estimate, Weak convergence



Denna post skapades 2011-08-05. Senast ändrad 2014-09-02.
CPL Pubid: 143811

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Numerisk analys

Chalmers infrastruktur

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On weak and strong convergence of numerical approximations of stochastic partial differential equations