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- Title
Strong convergence for an explicit fully‐discrete finite element approximation of the Cahn‐Hillard‐Cook equation with additive noise.
- Authors
Lin, Qiu; Qi, Ruisheng
- Abstract
In this paper, we consider an explicit fully‐discrete approximation of the Cahn–Hilliard–Cook (CHC) equation with additive noise, performed by a standard finite element method in space and a kind of nonlinearity‐tamed Euler scheme in time. The main result in this paper establishes strong convergence rates of the proposed scheme. The key ingredient in the proof of our main result is to employ uniform moment bounds for the numerical approximations. To the best of our knowledge, the main contribution of this work is the first result in the literature which establishes strong convergence for an explicit fully‐discrete finite element approximation of the CHC equation. Finally, numerical results are finally reported to confirm the previous theoretical findings.
- Subjects
EULER equations; FINITE element method; EQUATIONS; NOISE; CAHN-Hilliard-Cook equation
- Publication
Numerical Methods for Partial Differential Equations, 2024, Vol 40, Issue 1, p1
- ISSN
0749-159X
- Publication type
Article
- DOI
10.1002/num.23062