On the discretisation in time of the stochastic Allen–Cahn equation

Mihály Kovács, Stig Larsson and Fredrik Lindgren

Mathematische Nachrichten, 2018, vol. 291, issue 5-6, 966-995

Abstract: We consider the stochastic Allen–Cahn equation perturbed by smooth additive Gaussian noise in a bounded spatial domain with smooth boundary in dimension d≤3, and study the semidiscretisation in time of the equation by an Euler type split†step method with step size k>0. We show that the method converges strongly with a rate O(k12). By means of a perturbation argument, we also establish the strong convergence of the standard backward Euler scheme with the same rate.

Date: 2018
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