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# Strong convergence of a fully discrete finite element approximation of the stochastic Cahn-Hilliard equation

Daisuke Furihata ; Mihaly Kovacs (Institutionen för matematiska vetenskaper, matematik) ; Stig Larsson (Institutionen för matematiska vetenskaper, matematik) ; Fredrik Lindgren
(2016)
[Preprint]

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.

Nyckelord: stochastic partial differential equation; Cahn-Hilliard-Cook equation; additive noise; Wiener process; Finite element method, Euler method; time discretization; strong convergence

CPL Pubid: 246584

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# Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)