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Nonconforming multiscale finite element method for Stokes flows in heterogeneous media. Part I: Methodologies and numerical experiments

Muljadi, Bagus P.; Narski, J.; Lozinski, A.; Degond, P.


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Assistant Professor - Chemical & Environmental Engineering

J. Narski

A. Lozinski

P. Degond


The multiscale finite element method (MsFEM) is developed in the vein of the Crouzeix--Raviart element for solving viscous incompressible flows in genuine heterogeneous media. Such flows are relevant in many branches of engineering, often at multiple scales and at regions where analytical representations of the microscopic features of the flows are often unavailable. Full accounts of these problems heavily depend on the geometry of the system under consideration and are computationally expensive. Therefore, a method capable of solving multiscale features of the flow without confining itself to fine scale calculations is sought. 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 obstacles exempt from the need to implement any oversampling techniques. Additionally, the application of a penalization method makes it possible to avoid a complex unstructured domain and allows extensive use of simpler Cartesian meshes.


Muljadi, B. P., Narski, J., Lozinski, A., & Degond, P. (in press). Nonconforming multiscale finite element method for Stokes flows in heterogeneous media. Part I: Methodologies and numerical experiments. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 13(4),

Journal Article Type Article
Acceptance Date Aug 5, 2015
Online Publication Date Oct 22, 2015
Deposit Date Sep 19, 2017
Publicly Available Date Dec 4, 2018
Journal Multiscale Modeling and Simulation: a SIAM Interdisciplinary Journal
Print ISSN 1540-3459
Electronic ISSN 1540-3467
Publisher Society for Industrial and Applied Mathematics
Peer Reviewed Peer Reviewed
Volume 13
Issue 4
Keywords Crouzeix–Raviart element, Multiscale finite element method, Stokes equations, Penalization method
Public URL
Publisher URL
Copyright Statement Copyright information regarding this work can be found at the following address:
Additional Information c2015 Society for Industrial and Applied Mathematics


Nonconforming Multiscale Finite Element Method (33 Kb)

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