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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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
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author Khodadadian, Amirreza
Parvizi, Maryam
Abbaszadeh, Mostafa
Dehghan, Mehdi
Heitzinger, Clemens
author_facet Khodadadian, Amirreza
Parvizi, Maryam
Abbaszadeh, Mostafa
Dehghan, Mehdi
Heitzinger, Clemens
author_sort Khodadadian, Amirreza
collection PubMed
description 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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spelling pubmed-69366532020-01-09 A multilevel Monte Carlo finite element method for the stochastic Cahn–Hilliard–Cook equation Khodadadian, Amirreza Parvizi, Maryam Abbaszadeh, Mostafa Dehghan, Mehdi Heitzinger, Clemens Comput Mech Original Paper 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. Springer Berlin Heidelberg 2019-02-25 2019 /pmc/articles/PMC6936653/ /pubmed/31929667 http://dx.doi.org/10.1007/s00466-019-01688-1 Text en © The Author(s) 2019 OpenAccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Original Paper
Khodadadian, Amirreza
Parvizi, Maryam
Abbaszadeh, Mostafa
Dehghan, Mehdi
Heitzinger, Clemens
A multilevel Monte Carlo finite element method for the stochastic Cahn–Hilliard–Cook equation
title A multilevel Monte Carlo finite element method for the stochastic Cahn–Hilliard–Cook equation
title_full A multilevel Monte Carlo finite element method for the stochastic Cahn–Hilliard–Cook equation
title_fullStr A multilevel Monte Carlo finite element method for the stochastic Cahn–Hilliard–Cook equation
title_full_unstemmed A multilevel Monte Carlo finite element method for the stochastic Cahn–Hilliard–Cook equation
title_short A multilevel Monte Carlo finite element method for the stochastic Cahn–Hilliard–Cook equation
title_sort multilevel monte carlo finite element method for the stochastic cahn–hilliard–cook equation
topic Original Paper
url 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
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