TY - JOUR
T1 - ENRICHED NONCONFORMING MULTISCALE FINITE ELEMENT METHOD FOR STOKES FLOWS IN HETEROGENEOUS MEDIA BASED ON HIGH-ORDER WEIGHTING FUNCTIONS
AU - Feng, Qingqing
AU - Allaire, Gregoire
AU - Omnes, Pascal
N1 - Publisher Copyright:
© 2022 Society for Industrial and Applied Mathematics.
PY - 2022/1/1
Y1 - 2022/1/1
N2 - This paper addresses an enriched nonconforming multiscale finite element method (MsFEM) to solve viscous incompressible flow problems in genuine heterogeneous or porous media. In the work of [B. P. Muljadi, et al., Multiscale Model. Simul., 13 (2015), pp. 1146-1172] and [G. Jankowiak and A. Lozinski, arXiv:1802.04389, 2018], a nonconforming MsFEM has been first developed for Stokes problems in such media. Based on these works, we propose an innovative enriched nonconforming MsFEM where the approximation space of both velocity and pressure are enriched by weighting functions which are defined by polynomials of higher-degree. Numerical experiments show that this enriched nonconforming MsFEM improves significantly the accuracy of the nonconforming MsFEMs. Theoretically, this method provides a general framework which allows one to find a good compromise between the accuracy of the method and the computing costs, by varying the degrees of polynomials.
AB - This paper addresses an enriched nonconforming multiscale finite element method (MsFEM) to solve viscous incompressible flow problems in genuine heterogeneous or porous media. In the work of [B. P. Muljadi, et al., Multiscale Model. Simul., 13 (2015), pp. 1146-1172] and [G. Jankowiak and A. Lozinski, arXiv:1802.04389, 2018], a nonconforming MsFEM has been first developed for Stokes problems in such media. Based on these works, we propose an innovative enriched nonconforming MsFEM where the approximation space of both velocity and pressure are enriched by weighting functions which are defined by polynomials of higher-degree. Numerical experiments show that this enriched nonconforming MsFEM improves significantly the accuracy of the nonconforming MsFEMs. Theoretically, this method provides a general framework which allows one to find a good compromise between the accuracy of the method and the computing costs, by varying the degrees of polynomials.
KW - Crouzeix-Raviart element
KW - Multiscale finite element method
KW - Stokes flows
U2 - 10.1137/21M141926X
DO - 10.1137/21M141926X
M3 - Article
AN - SCOPUS:85130874084
SN - 1540-3459
VL - 20
SP - 462
EP - 492
JO - Multiscale Modeling and Simulation
JF - Multiscale Modeling and Simulation
IS - 1
ER -