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Strong convergence of a fully discrete finite element approximation of the stochastic cahn–hilliard equation

Journal article
Authors Daisuke Furihata
Mihaly Kovacs
Stig Larsson
Fredrik Lindgren
Published in SIAM Journal on Numerical Analysis
Volume 56
Pages 708-731
ISSN 0036-1429
Publication year 2018
Published at Department of Mathematical Sciences
Pages 708-731
Language en
Links https://doi.org/10.1137/17M1121627
Keywords Additive noise, Cahn–Hilliard–Cook equation, Euler method, Finite element method, Stochastic partial differential equation, Strong convergence, Time discretization, Wiener process
Subject categories Probability Theory and Statistics, Computational Mathematics, Mathematical Analysis

Abstract

© 2018 Society for Industrial and Applied Mathematics. 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.

Page Manager: Webmaster|Last update: 9/11/2012
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