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

Degond, Pierre; Lozinski, Alexei; Muljadi, Bagus Putra; Narski, Jacek

Authors

Pierre Degond

Alexei Lozinski

Bagus Putra Muljadi

Jacek Narski



Abstract

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.

Journal Article Type Article
Journal Communications in Computational Physics
Electronic ISSN 1991-7120
Peer Reviewed Peer Reviewed
Volume 17
Issue 4
APA6 Citation Degond, P., Lozinski, A., Muljadi, B. P., & Narski, J. (in press). Crouzeix-Raviart MsFEM with bubble functions for diffusion and advection-diffusion in perforated media. Communications in Computational Physics, 17(4), https://doi.org/10.4208/cicp.2014.m299
DOI https://doi.org/10.4208/cicp.2014.m299
Keywords Multiscale finite element method, Crouzeix-Raviart, Porous media, Bubble function
Publisher URL 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
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information This article is for private research and study and may not be distributed further. It has been accepted for publication and will appear in a revised form subject to input from the Journal's editor

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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