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On the backward Euler approximation of the stochastic Allen-Cahn equation

Mihaly Kovacs ; Stig Larsson (Institutionen för matematiska vetenskaper, matematik) ; Fredrik Lindgren (Institutionen för matematiska vetenskaper, matematik)
(2013)
[Preprint]

We consider the stochastic Allen-Cahn equation perturbed by smooth additive Gaussian noise in a spatial domain with smooth boundary in dimension d ≤ 3, and study the semidiscretization in time of the equation by an implicit Euler method. We show that the method converges pathwise with a rate O(∆t^γ) for any γ < 1/2. We also prove that the scheme converges uniformly in the strong L^p-sense but with no rate given.

Nyckelord: Stochastic partial differential equation, Allen-Cahn equation, additive noise, Wiener process, Euler method, pathwise convergence, strong convergence, factorization method



Denna post skapades 2013-11-14. Senast ändrad 2014-09-02.
CPL Pubid: 186691

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Numerisk analys

Chalmers infrastruktur