Crouzeix-Raviart MsFEM with bubble functions for diffusion and advection-diffusion in perforated media

The adaptation of Crouzeix-Raviart finite element in the context of multi-scale finite element method (MsFEM) is studied and implemented on diffusion and advection-diffusion problems in perforated media. It is known that the approximation of boundary condition on coarse element edges when computing...

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Main Authors: Degond, Pierre, Lozinski, Alexei, Muljadi, Bagus Putra, Narski, Jacek
Format: Article
Published: Cambridge University Press 2015
Subjects:
Online Access:https://eprints.nottingham.ac.uk/46425/
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author Degond, Pierre
Lozinski, Alexei
Muljadi, Bagus Putra
Narski, Jacek
author_facet Degond, Pierre
Lozinski, Alexei
Muljadi, Bagus Putra
Narski, Jacek
author_sort Degond, Pierre
building Nottingham Research Data Repository
collection Online Access
description The adaptation of Crouzeix-Raviart finite element in the context of multi-scale finite element method (MsFEM) is studied and implemented on diffusion and advection-diffusion problems in perforated media. It is known that the approximation of boundary condition on coarse element edges when computing the multiscale basis functions critically influences the eventual accuracy of any MsFEM approaches. The weakly enforced continuity of Crouzeix-Raviart function space across element edges leads to a natural boundary condition for the multiscale basis functions which relaxes the sensitivity of our method to complex patterns of perforations. Another ingredient to our method is the application of bubble functions which is shown to be instrumental in maintaining high accuracy amid dense perforations. Additionally, the application of penalization method makes it possible to avoid complex unstructured domain and allows extensive use of simpler Cartesian meshes.
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spelling nottingham-464252020-05-04T17:05:41Z https://eprints.nottingham.ac.uk/46425/ Crouzeix-Raviart MsFEM with bubble functions for diffusion and advection-diffusion in perforated media Degond, Pierre Lozinski, Alexei Muljadi, Bagus Putra Narski, Jacek The adaptation of Crouzeix-Raviart finite element in the context of multi-scale finite element method (MsFEM) is studied and implemented on diffusion and advection-diffusion problems in perforated media. It is known that the approximation of boundary condition on coarse element edges when computing the multiscale basis functions critically influences the eventual accuracy of any MsFEM approaches. The weakly enforced continuity of Crouzeix-Raviart function space across element edges leads to a natural boundary condition for the multiscale basis functions which relaxes the sensitivity of our method to complex patterns of perforations. Another ingredient to our method is the application of bubble functions which is shown to be instrumental in maintaining high accuracy amid dense perforations. Additionally, the application of penalization method makes it possible to avoid complex unstructured domain and allows extensive use of simpler Cartesian meshes. Cambridge University Press 2015-04-30 Article PeerReviewed Degond, Pierre, Lozinski, Alexei, Muljadi, Bagus Putra and Narski, Jacek (2015) Crouzeix-Raviart MsFEM with bubble functions for diffusion and advection-diffusion in perforated media. Communications in Computational Physics, 17 (4). pp. 887-907. ISSN 1991-7120 Multiscale finite element method Crouzeix-Raviart Porous media Bubble function https://www.cambridge.org/core/journals/communications-in-computational-physics/article/crouzeix-raviart-msfem-with-bubble-functions-for-diffusion-and-advection-diffusion-in-perforated-media/56CA454FD91CC0A3AC4AB2B1FCF94DA5 doi:10.4208/cicp.2014.m299 doi:10.4208/cicp.2014.m299
spellingShingle Multiscale finite element method
Crouzeix-Raviart
Porous media
Bubble function
Degond, Pierre
Lozinski, Alexei
Muljadi, Bagus Putra
Narski, Jacek
Crouzeix-Raviart MsFEM with bubble functions for diffusion and advection-diffusion in perforated media
title Crouzeix-Raviart MsFEM with bubble functions for diffusion and advection-diffusion in perforated media
title_full Crouzeix-Raviart MsFEM with bubble functions for diffusion and advection-diffusion in perforated media
title_fullStr Crouzeix-Raviart MsFEM with bubble functions for diffusion and advection-diffusion in perforated media
title_full_unstemmed Crouzeix-Raviart MsFEM with bubble functions for diffusion and advection-diffusion in perforated media
title_short Crouzeix-Raviart MsFEM with bubble functions for diffusion and advection-diffusion in perforated media
title_sort crouzeix-raviart msfem with bubble functions for diffusion and advection-diffusion in perforated media
topic Multiscale finite element method
Crouzeix-Raviart
Porous media
Bubble function
url https://eprints.nottingham.ac.uk/46425/
https://eprints.nottingham.ac.uk/46425/
https://eprints.nottingham.ac.uk/46425/