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Finite-element approximation of the linearized Cahn-Hilliard-Cook equation

Stig Larsson (Institutionen för matematiska vetenskaper, matematik) ; Ali Mesforush
IMA Journal of Numerical Analysis (0272-4979). Vol. 31 (2011), 4, p. 1315-1333.
[Artikel, refereegranskad vetenskaplig]

The linearized Cahn–Hilliard–Cook equation is discretized in the spatial variables by a standard finite-element method. Strong convergence estimates are proved under suitable assumptions on the covariance operator of the Wiener process, which is driving the equation. Backward Euler time stepping is also studied. The analysis is set in a framework based on analytic semigroups. The main effort is spent on proving detailed error bounds for the corresponding deterministic Cahn–Hilliard equation. The results should be interpreted as results on the approximation of the stochastic convolution, which is a part of the mild solution of the nonlinear Cahn–Hilliard–Cook equation.

Nyckelord: Cahn–Hilliard–Cook equation, stochastic convolution, Wiener process, finite-element method, backward Euler method, mean square error estimate, strong convergence

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Denna post skapades 2011-05-10. Senast ändrad 2014-09-02.
CPL Pubid: 140523


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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)


Numerisk analys

Chalmers infrastruktur