Numerical approximation of the stochastic Cahn-Hilliard equation near the sharp interface limit

Antonopoulou D, Banas L, Nurnberg R, Prohl A (2021)
Numerische Mathematik 147(3): 505-551.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Antonopoulou, Dimitra; Banas, LubomirUniBi; Nurnberg, Robert; Prohl, Andreas
Abstract / Bemerkung
We consider the stochastic Cahn-Hilliard equation with additive noise term epsilon(gamma) g (W)over dot (gamma > 0) that scales with the interfacial width parameter epsilon. We verify strong error estimates for a gradient flow structure-inheriting time-implicit discretization, where epsilon(-1) only enters polynomially; the proof is based on higher-moment estimates for iterates, and a (discrete) spectral estimate for its deterministic counterpart. For. sufficiently large, convergence in probability of iterates towards the deterministic Hele-Shaw/Mullins-Sekerka problem in the sharp-interface limit epsilon -> 0 is shown. These convergence results are partly generalized to a fully discrete finite element based discretization. We complement the theoretical results by computational studies to provide practical evidence concerning the effect of noise (depending on its 'strength' gamma) on the geometric evolution in the sharp-interface limit. For this purpose we compare the simulations with those from a fully discrete finite element numerical scheme for the (stochastic) Mullins-Sekerka problem. The computational results indicate that the limit for gamma >= 1 is the deterministic problem, and for gamma = 0 we obtain agreement with a (new) stochastic version of the Mullins-Sekerka problem.
Erscheinungsjahr
2021
Zeitschriftentitel
Numerische Mathematik
Band
147
Ausgabe
3
Seite(n)
505-551
ISSN
0029-599X
eISSN
0945-3245
Page URI
https://pub.uni-bielefeld.de/record/2952722

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Antonopoulou D, Banas L, Nurnberg R, Prohl A. Numerical approximation of the stochastic Cahn-Hilliard equation near the sharp interface limit. Numerische Mathematik . 2021;147(3):505-551.
Antonopoulou, D., Banas, L., Nurnberg, R., & Prohl, A. (2021). Numerical approximation of the stochastic Cahn-Hilliard equation near the sharp interface limit. Numerische Mathematik , 147(3), 505-551. https://doi.org/10.1007/s00211-021-01179-7
Antonopoulou, D., Banas, L., Nurnberg, R., and Prohl, A. (2021). Numerical approximation of the stochastic Cahn-Hilliard equation near the sharp interface limit. Numerische Mathematik 147, 505-551.
Antonopoulou, D., et al., 2021. Numerical approximation of the stochastic Cahn-Hilliard equation near the sharp interface limit. Numerische Mathematik , 147(3), p 505-551.
D. Antonopoulou, et al., “Numerical approximation of the stochastic Cahn-Hilliard equation near the sharp interface limit”, Numerische Mathematik , vol. 147, 2021, pp. 505-551.
Antonopoulou, D., Banas, L., Nurnberg, R., Prohl, A.: Numerical approximation of the stochastic Cahn-Hilliard equation near the sharp interface limit. Numerische Mathematik . 147, 505-551 (2021).
Antonopoulou, Dimitra, Banas, Lubomir, Nurnberg, Robert, and Prohl, Andreas. “Numerical approximation of the stochastic Cahn-Hilliard equation near the sharp interface limit”. Numerische Mathematik 147.3 (2021): 505-551.

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