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Oversampling for the Multiscale Finite Element Method [PDF]
Multiscale Modeling & Simulation, 2013 This paper reviews standard oversampling strategies as performed in the Multiscale Finite Element Method (MsFEM). Common to those approaches is that the oversampling is performed in the full space restricted to a patch but including coarse finite element functions.
Henning, Patrick, Peterseim, Daniel
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An Adaptive Multiscale Finite Element Method [PDF]
Multiscale Modeling & Simulation, 2014 This work is devoted to an adaptive multiscale finite element method (MsFEM) for solving elliptic problems with rapidly oscillating coeefficients. Starting from a general version of the MsFEM with oversampling, we de- rive an a posteriori estimate for the H1-error between the exact solution of the problem and a corresponding MsFEM approximation.
Henning, Patrick +2 more
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Generalized Multiscale Finite Element Method for Elastic Wave Propagation in the Frequency Domain
Computation, 2020 In this work, we consider elastic wave propagation in fractured media. The mathematical model is described by the Helmholtz problem related to wave propagation with specific interface conditions (Linear Slip Model, LSM) on the fracture in the frequency ...
Uygulana Gavrilieva +2 more
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A dual-mesh multiscale finite element method for simulating nodal Darcy velocities in aquifers
Yantu gongcheng xuebao, 2020 A dual-mesh multiscale finite element method (D-MSFEM) is developed to simulate nodal Darcy velocities in aquifers. It is a combination of the multiscale finite element method (MSFEM) and the dual-mesh finite element method (D-FEM).
ZHAO Wen-feng 1, XIE Yi-fan 2, WU Ji-chun 1
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Mathematics, 2021 In this paper, we present a multiscale model reduction technique for unsaturated filtration problem in fractured porous media using an Online Generalized Multiscale finite element method. The flow problem in unsaturated soils is described by the Richards
Denis Spiridonov +3 more
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GENERALIZED MULTISCALE FINITE ELEMENT METHODS: OVERSAMPLING STRATEGIES [PDF]
International Journal for Multiscale Computational Engineering, 2014 In this paper, we propose oversampling strategies in the Generalized Multiscale Finite Element Method (GMsFEM) framework. The GMsFEM, which has been recently introduced in [12], allows solving multiscale parameter-dependent problems at a reduced computational cost by constructing a reduced-order representation of the solution on a coarse grid. The main
Efendiev, Yalchin R. +3 more
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A Combined Finite Element and Multiscale Finite Element Method for the Multiscale Elliptic Problems [PDF]
Multiscale Modeling & Simulation, 2014 The oversampling multiscale finite element method (MsFEM) is one of the most popular methods for simulating composite materials and flows in porous media which may have many scales. But the method may be inapplicable or inefficient in some portions of the computational domain, e.g., near the domain boundary or near long narrow channels inside the ...
Deng, Weibing, Wu, Haijun
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Online Multiscale Finite Element Simulation of Thermo-Mechanical Model with Phase Change
Computation, 2023 This paper presents a thermo-mechanical model with phase transition considering changes in the mechanical properties of the medium. The proposed thermo-mechanical model is described by a system of partial differential equations for temperature and ...
Dmitry Ammosov, Maria Vasilyeva
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Mixed Generalized Multiscale Finite Element Methods and Applications [PDF]
Multiscale Modeling & Simulation, 2015 In this paper, we present a mixed Generalized Multiscale Finite Element Method (GMsFEM) for solving flow in heterogeneous media. Our approach constructs multiscale basis functions following a GMsFEM framework and couples these basis functions using a mixed finite element method, which allows us to obtain a mass conservative velocity field. To construct
Chung, Eric T. +2 more
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Computation, 2020 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 ...
Valentin Alekseev +4 more
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