Strong convergence of a fully discrete finite element approximation of the stochastic Cahn-Hilliard equation
Preprint, 2016
We consider the stochastic Cahn-Hilliard equation driven by additive Gaussian noise in a convex domain with polygonal boundary in dimension $d\le 3$. We discretize the equation using a standard finite element method is space and a fully implicit backward Euler method in time. By proving optimal error estimates on subsets of the probability space with arbitrarily large probability and uniform-in-time moment bounds we show that the numerical solution converges strongly to the solution as the discretization parameters tend to zero.
Cahn-Hilliard-Cook equation
Euler method
time discretization
additive noise
Finite element method
stochastic partial differential equation
Wiener process
strong convergence
Author
Daisuke Furihata
Mihaly Kovacs
Chalmers, Mathematical Sciences, Mathematics
University of Gothenburg
Stig Larsson
Chalmers, Mathematical Sciences, Mathematics
University of Gothenburg
Fredrik Lindgren
Subject Categories
Computational Mathematics
Probability Theory and Statistics
Roots
Basic sciences