Crouzeix-Raviart MsFEM with Bubble Functions for Diffusion and Advection-Diffusion in Perforated Media. (30th April 2015)

• Record Type: Journal Article
• Authors: Degond, Pierre; Lozinski, Alexei; Muljadi, Bagus Putra; Narski, Jacek
• Is Part Of: Communications in computational physics. Volume 17:Number 4(2015:Apr.)
• Page Start: 887
• Page End: 907
• Publication Date: 2015-04-30
• Subjects: Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.2014.m299
• Languages: English
• ISSNs: 1815-2406

Abstract

<abstract abstract-type="normal"> <title>Abstract</title> <p>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.</p> </abstract>