Results 11 to 20 of about 5,178 (170)
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
openaire +3 more sources
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
doaj +1 more source
Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods [PDF]
Journal of Computational Physics, 2016 In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. Due to page limitations, the overview focuses on a few related methods and is not intended to be comprehensive.
Chung, Eric +2 more
openaire +4 more sources
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
doaj +1 more source
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
openaire +4 more sources
Convergence of a Nonconforming Multiscale Finite Element Method [PDF]
SIAM Journal on Numerical Analysis, 2000 The multiscale finite element method introduced to capture the large scale solutions of elliptic boundary value problems with highly oscillatory coefficients is considered. The leading order error in this approach is caused by the ``resonant sampling'', which leads to large error when the mesh size is close to the small scale of the continuous problem.
Efendiev, Yalchin R. +2 more
openaire +2 more sources
Mathematical Modelling and Analysis, 2015 In this paper, a modified method of characteristics variational multiscale (MMOCVMS) finite element method is presented for the time dependent NavierStokes problems, which is leaded by combining the characteristics time discretization with the ...
Zhiyong Si, Yunxia Wang, Xinlong Feng
doaj +1 more source
Constraint Energy Minimizing Generalized Multiscale Finite Element Method [PDF]
Computer Methods in Applied Mechanics and Engineering, 2018 The main goal of this paper is to design multiscale basis functions within GMsFEM framework such that the convergence of method is independent of the contrast and linearly decreases with respect to mesh size if oversampling size is appropriately chosen. We would like to show a mesh-dependent convergence with a minimal number of basis functions.
Chung, Eric T. +2 more
openaire +3 more sources
Computation, 2015 In this paper, we develop a mass conservative multiscale method for coupled flow and transport in heterogeneous porous media. We consider a coupled system consisting of a convection-dominated transport equation and a flow equation.
Eric T. Chung +3 more
doaj +1 more source
Generalized multiscale finite element method for elasticity equations [PDF]
GEM - International Journal on Geomathematics, 2014 In this paper, we discuss the application of Generalized Multiscale Finite Element Method (GMsFEM) to elasticity equation in heterogeneous media. Our applications are motivated by elastic wave propagation in subsurface where the subsurface properties can be highly heterogeneous and have high contrast. We present the construction of main ingredients for
Chung, Eric T. +2 more
openaire +4 more sources