Strong convergence of a fully discrete finite element approximation of the stochastic cahn–hilliard equation
Artikel i vetenskaplig tidskrift, 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

Författare

Daisuke Furihata

Osaka University

Mihaly Kovacs

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Stig Larsson

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Fredrik Lindgren

Osaka University

SIAM Journal on Numerical Analysis

0036-1429 (ISSN) 1095-7170 (eISSN)

Vol. 56 708-731

Ämneskategorier

Beräkningsmatematik

Sannolikhetsteori och statistik

Matematisk analys

DOI

10.1137/17M1121627