ENRICHED NONCONFORMING MULTISCALE FINITE ELEMENT METHOD FOR STOKES FLOWS IN HETEROGENEOUS MEDIA BASED ON HIGH-ORDER WEIGHTING FUNCTIONS

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.

Automated summary

This paper presents an enriched nonconforming multiscale finite element method (MsFEM) for solving viscous incompressible flow problems in genuine heterogeneous or porous media. By using weighting functions defined by higher-degree polynomials, this method significantly improves the accuracy of nonconforming MsFEMs while finding a good compromise between accuracy and computing costs.