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


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 2 708-731

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Mathematical Analysis



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