Strong convergence of a fully discrete finite element approximation of the stochastic cahn–hilliard equation
Journal article, 2018
We consider the stochastic Cahn–Hilliard equation driven by additive Gaussian noise in a convex domain with polygonal boundary in dimension d ≤ 3. We discretize the equation using a standard finite element method in 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.
Time discretization
Finite element method
Strong convergence
Stochastic partial differential equation
Cahn–Hilliard–Cook equation
Euler method
Wiener process
Additive noise
Author
Daisuke Furihata
Osaka University
Mihaly Kovacs
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
Stig Larsson
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
Fredrik Lindgren
Osaka University
SIAM Journal on Numerical Analysis
0036-1429 (ISSN) 1095-7170 (eISSN)
Vol. 56 2 708-731Subject Categories
Computational Mathematics
Probability Theory and Statistics
Mathematical Analysis
DOI
10.1137/17M1121627