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 2 323-338Subject Categories (SSIF 2011)
Computational Mathematics
Roots
Basic sciences
DOI
10.1239/jap/1437658601