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

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

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.

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

• Journal Article Type: Article
• Acceptance Date: Jun 11, 2014
• Online Publication Date: Apr 30, 2015
• Deposit Date: Sep 21, 2017
• Publicly Available Date: Sep 21, 2017
• Journal: Communications in Computational Physics
• Electronic ISSN: 1991-7120
• Peer Reviewed: Peer Reviewed
• Volume: 17
• Issue: 4
• DOI: https://doi.org/10.4208/cicp.2014.m299
• Keywords: Multiscale finite element method, Crouzeix-Raviart, Porous media, Bubble function
• Public URL: https://nottingham-repository.worktribe.com/output/748796
• 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
• 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