On the backward Euler approximation of the stochastic Allen-Cahn equation
Preprint, 2013

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.

pathwise convergence

strong convergence

additive noise

Stochastic partial differential equation

Wiener process

factorization method

Allen-Cahn equation

Euler method

Författare

Stig Larsson

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Fredrik Lindgren

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Ämneskategorier

Beräkningsmatematik

Fundament

Grundläggande vetenskaper

Mer information

Skapat

2017-10-07