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Original version
Khodadadian, A.; Parvizi, M.; Abbaszadeh, M.; Dehghan, M.; Heitzinger, C.: A multilevel Monte Carlo finite element method for the stochastic Cahn–Hilliard–Cook equation. In: Computational Mechanics 64 (2019), Nr. 4, S. 937-949. DOI: https://doi.org/10.1007/s00466-019-01688-1
Repository version
To cite the version in the repository, please use this identifier:
https://doi.org/10.15488/4741
Files in this item
| Abstract: | |
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In this paper, we employ the multilevel Monte Carlo finite element method to solve the stochastic Cahn–Hilliard–Cook equation. The Ciarlet–Raviart mixed finite element method is applied to solve the fourth-order equation. In order to estimate the mild solution, we use finite elements for space discretization and the semi-implicit Euler–Maruyama method in time. For the stochastic scheme, we use the multilevel method to decrease the computational cost (compared to the Monte Carlo method). We implement the method to solve three specific numerical examples (both two- and three dimensional) and study the effect of different noise measures. © 2019, The Author(s).
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| License of this version: | CC BY 4.0 Unported - https://creativecommons.org/licenses/by/4.0/ |
| Publication type: | Article |
| Publishing status: | publishedVersion |
| Publication date: | 2019 |
| Keywords english: | Cahn–Hilliard–Cook equation, Euler–Maruyama method, Finite element, Multilevel Monte Carlo, Time discretization, Monte Carlo methods, Numerical methods, Stochastic systems, Computational costs, Fourth-order equations, Mild solution, Mixed finite element methods, Monte Carlo finite element method, Multilevel method, Space discretizations, Time discretization, Finite element method |
| DDC: | 530 | Physik, 004 | Informatik |
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Fakultät für Mathematik und Physik
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