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


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


Basic sciences

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