A multilevel Monte Carlo finite element method for the stochastic Cahn–Hilliard–Cook equation

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 discr...

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Detalles Bibliográficos
Autores principales: Khodadadian, Amirreza, Parvizi, Maryam, Abbaszadeh, Mostafa, Dehghan, Mehdi, Heitzinger, Clemens
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2019
Materias:
Original Paper
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6936653/
https://www.ncbi.nlm.nih.gov/pubmed/31929667
http://dx.doi.org/10.1007/s00466-019-01688-1
Descripción
Sumario: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.

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