| Abstract: |
| We discuss the numerical approximation of the stochastic Cahn-Hilliard equation with a singular double-obstacle potential and multiplicative conservative noise. We propose a regularized fully discrete finite element approximation scheme for the problem and show that is satisfies stability estimates which are uniform with respect to the discretisation parameters. We show convergence of the approximation for vanishing discretisation parameters towards a regularised version of the singular stochastic Cahn-Hilliard equation by monotonicity arguments. Owing to a uniform $H^1$-estimate for the regularised problem we then establish convergence of the regularised solution to the probabilistically strong solution of the stochastic Cahn-Hilliard equation with double-obstacle potential. We also present numerical simulations where we compare the regularised numerical approximation to its unregularised counterpart and illustrate the effect of the conservative noise. |
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