The heterogeneous multiscale finite element method for elliptic homogenization problems in perforated domains

2009 ◽  
Vol 113 (4) ◽  
pp. 601-629 ◽  
Author(s):  
Patrick Henning ◽  
Mario Ohlberger
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Perforated Domains ◽  
Multiscale Finite Element Method ◽  
Multiscale Finite Element ◽  
Heterogeneous Multiscale ◽  
Homogenization Problems ◽  
Element Method

scholarly journals Mixed Generalized Multiscale Finite Element Method for a Simplified Magnetohydrodynamics Problem in Perforated Domains

Computation ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 58
Author(s):  
Valentin Alekseev ◽  
Qili Tang ◽  
Maria Vasilyeva ◽  
Eric T. Chung ◽  
Yalchin Efendiev
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Model Problem ◽  
Mixed Finite Element ◽  
Basis Functions ◽  
Fine Grid ◽  
Perforated Domains ◽  
Multiscale Finite Element Method ◽  
Multiscale Finite Element ◽  
Element Method

In this paper, we consider a coupled system of equations that describes simplified magnetohydrodynamics (MHD) problem in perforated domains. We construct a fine grid that resolves the perforations on the grid level in order to use a traditional approximation. For the solution on the fine grid, we construct approximation using the mixed finite element method. To reduce the size of the fine grid system, we will develop a Mixed Generalized Multiscale Finite Element Method (Mixed GMsFEM). The method differs from existing approaches and requires some modifications to represent the flow and magnetic fields. Numerical results are presented for a two-dimensional model problem in perforated domains. This model problem is a special case for the general 3D problem. We study the influence of the number of multiscale basis functions on the accuracy of the method and show that the proposed method provides a good accuracy with few basis functions.

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