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arXiv · 1612.09459

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

Daisuke Furihata·Mihály Kovács·Stig Larsson·Fredrik Lindgren
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Abstract

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 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.

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Daisuke Furihata, Mihály Kovács, Stig Larsson, Fredrik Lindgren. 2016-12-30. Strong convergence of a fully discrete finite element approximation of the stochastic Cahn-Hilliard equation. https://doi.org/10.1137/17m1121627

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