Volume 17, Issue 4
Crouzeix-Raviart MsFEM with Bubble Functions for Diffusion and Advection-Diffusion in Perforated Media

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

Commun. Comput. Phys., 17 (2015), pp. 887-907.

Published online: 2018-04

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  • Abstract

The adaptation of Crouzeix-Raviart finite element in the context of multiscale 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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@Article{CiCP-17-887, author = {}, title = {Crouzeix-Raviart MsFEM with Bubble Functions for Diffusion and Advection-Diffusion in Perforated Media}, journal = {Communications in Computational Physics}, year = {2018}, volume = {17}, number = {4}, pages = {887--907}, abstract = {

The adaptation of Crouzeix-Raviart finite element in the context of multiscale 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2014.m299}, url = {http://global-sci.org/intro/article_detail/cicp/10982.html} }
TY - JOUR T1 - Crouzeix-Raviart MsFEM with Bubble Functions for Diffusion and Advection-Diffusion in Perforated Media JO - Communications in Computational Physics VL - 4 SP - 887 EP - 907 PY - 2018 DA - 2018/04 SN - 17 DO - http://dor.org/10.4208/cicp.2014.m299 UR - https://global-sci.org/intro/article_detail/cicp/10982.html KW - AB -

The adaptation of Crouzeix-Raviart finite element in the context of multiscale 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.

Pierre Degond, Alexei Lozinski, Bagus Putra Muljadi & Jacek Narski. (2020). Crouzeix-Raviart MsFEM with Bubble Functions for Diffusion and Advection-Diffusion in Perforated Media. Communications in Computational Physics. 17 (4). 887-907. doi:10.4208/cicp.2014.m299
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