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.
Wiener process
Stochastic partial differential equation
factorization method
additive noise
strong convergence
Allen-Cahn equation
pathwise convergence
Euler method
Author
Mihaly Kovacs
University of Otago
Stig Larsson
Chalmers, Mathematical Sciences, Mathematics
University of Gothenburg
Fredrik Lindgren
University of Gothenburg
Chalmers, Mathematical Sciences, Mathematics
Journal of Applied Probability
0021-9002 (ISSN)
Vol. 52 2 323-338Subject Categories
Computational Mathematics
Roots
Basic sciences
DOI
10.1239/jap/1437658601