On the backward Euler approximation of the stochastic Allen-Cahn equation
Journal article, 2015

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(Δt^γ) for any γ < ½. We also prove that the scheme converges uniformly in the strong L^p -sense but with no rate given.

Allen-Cahn equation

pathwise convergence

Wiener process

Euler method

additive noise

factorization method

Stochastic partial differential equation

strong convergence

Author

Mihaly Kovacs

University of Otago

Stig Larsson

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Fredrik Lindgren

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Journal of Applied Probability

0021-9002 (ISSN)

Vol. 52 2 323-338

Subject Categories

Computational Mathematics

Roots

Basic sciences

DOI

10.1239/jap/1437658601

More information

Created

10/7/2017