# 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

Finite element method

stochastic partial differential equation

Wiener process

strong convergence

## Författare

#### Mihaly Kovacs

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

#### Ämneskategorier

Beräkningsmatematik

Sannolikhetsteori och statistik

#### Fundament

Grundläggande vetenskaper

2017-10-07