On the backward Euler approximation of the stochastic Allen-Cahn equation
Artikel i vetenskaplig tidskrift, 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
Författare
Mihaly Kovacs
University of Otago
Stig Larsson
Chalmers, Matematiska vetenskaper, Matematik
Göteborgs universitet
Fredrik Lindgren
Göteborgs universitet
Chalmers, Matematiska vetenskaper, Matematik
Journal of Applied Probability
0021-9002 (ISSN)
Vol. 52 2 323-338Ämneskategorier
Beräkningsmatematik
Fundament
Grundläggande vetenskaper
DOI
10.1239/jap/1437658601