Nonconforming multiscale finite element method for Stokes flows in heterogeneous media. Part I: Methodologies and numerical experiments
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 representa...
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| Language: | English English |
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Society for Industrial and Applied Mathematics
2015
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| Online Access: | https://eprints.nottingham.ac.uk/46423/ |
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| author | Muljadi, Bagus P. Narski, J. Lozinski, A. Degond, P. |
| author_facet | Muljadi, Bagus P. Narski, J. Lozinski, A. Degond, P. |
| author_sort | Muljadi, Bagus P. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:02:03Z |
| format | Article |
| id | nottingham-46423 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-14T20:02:03Z |
| publishDate | 2015 |
| publisher | Society for Industrial and Applied Mathematics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-464232018-12-04T17:57:55Z https://eprints.nottingham.ac.uk/46423/ 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. 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. Society for Industrial and Applied Mathematics 2015-10-22 Article PeerReviewed application/pdf en https://eprints.nottingham.ac.uk/46423/2/Stokes%20flows%2014096428X.pdf application/pdf en https://eprints.nottingham.ac.uk/46423/1/14096428X Muljadi, Bagus P., Narski, J., Lozinski, A. and Degond, P. (2015) 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). pp. 1146-1172. ISSN 1540-3467 Crouzeix–Raviart element Multiscale finite element method Stokes equations Penalization method https://doi.org/10.1137/14096428X doi:10.1137/14096428X doi:10.1137/14096428X |
| spellingShingle | Crouzeix–Raviart element Multiscale finite element method Stokes equations Penalization method Muljadi, Bagus P. Narski, J. Lozinski, A. Degond, P. Nonconforming multiscale finite element method for Stokes flows in heterogeneous media. Part I: Methodologies and numerical experiments |
| title | Nonconforming multiscale finite element method for Stokes flows in heterogeneous media. Part I: Methodologies and numerical experiments |
| title_full | Nonconforming multiscale finite element method for Stokes flows in heterogeneous media. Part I: Methodologies and numerical experiments |
| title_fullStr | Nonconforming multiscale finite element method for Stokes flows in heterogeneous media. Part I: Methodologies and numerical experiments |
| title_full_unstemmed | Nonconforming multiscale finite element method for Stokes flows in heterogeneous media. Part I: Methodologies and numerical experiments |
| title_short | Nonconforming multiscale finite element method for Stokes flows in heterogeneous media. Part I: Methodologies and numerical experiments |
| title_sort | nonconforming multiscale finite element method for stokes flows in heterogeneous media. part i: methodologies and numerical experiments |
| topic | Crouzeix–Raviart element Multiscale finite element method Stokes equations Penalization method |
| url | https://eprints.nottingham.ac.uk/46423/ https://eprints.nottingham.ac.uk/46423/ https://eprints.nottingham.ac.uk/46423/ |