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

Author

Stig Larsson

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Fredrik Lindgren

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Subject Categories

Computational Mathematics

Roots

Basic sciences

More information

Created

10/7/2017