Related papers: Non-Conforming Multiscale Finite Element Method fo…
This paper is dedicated to the rigorous numerical analysis of a Multiscale Finite Element Method (MsFEM) for the Stokes system, when dealing with highly heterogeneous media, as proposed in [B.P.~Muljadi et al., arXiv:1404.2837]. The method…
The adaptation of Crouzeix - Raviart finite element in the context of multiscale finite element method (MsFEM) is studied and implemented on diffusion and advection-diffusion problems in perforated media. It is known that the approximation…
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…
We develop a family of expanded mixed Multiscale Finite Element Methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed Multiscale Finite Element formulation in the sense…
Accurate prediction of the macroscopic flow parameters needed to describe flow in porous media relies on a good knowledge of flow field distribution at a much smaller scale---in the pore spaces. The extent of the inertial effect in the pore…
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…
This paper explores the application of the multiscale finite element method (MsFEM) to address steady-state Stokes-Darcy problems with BJS interface conditions in highly heterogeneous porous media. We assume the existence of multiscale…
Multiscale Finite Element Methods (MsFEM) are finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions which generate a specific discretization space, and next…
In this paper, we examine the effectiveness of classic multiscale finite element method (MsFEM) (Hou and Wu, 1997; Hou et al., 1999) for mixed Dirichlet-Neumann, Robin and hemivariational inequality boundary problems. Constructing so-called…
Multiscale Finite Element Methods (MsFEMs) are now well-established finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions that generate a suitable…
We follow up on our previous work [C. Le Bris, F. Legoll and A. Lozinski, Chinese Annals of Mathematics 2013] where we have studied a multiscale finite element (MsFEM) type method in the vein of the classical Crouzeix-Raviart finite element…
In this paper, we consider the incompressible Stokes flow problem in a perforated domain and employ the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) to solve this problem. The proposed method…
In this paper, we consider the numerical solution of poroelasticity problems that are of Biot type and develop a general algorithm for solving coupled systems. We discuss the challenges associated with mechanics and flow problems in…
This paper presents a novel mass-conservative mixed multiscale method for solving flow equations in heterogeneous porous media. The media properties (the permeability) contain multiple scales and high contrast. The proposed method solves…
We consider an advection-diffusion equation that is advection-dominated and posed on a perforated domain. On the boundary of the perforations, we set either homogeneous Dirichlet or homogeneous Neumann conditions. The purpose of this work…
In this paper, we study the development of efficient multiscale methods for flows in heterogeneous media. Our approach uses the Generalized Multiscale Finite Element (GMsFEM) framework. The main idea of GMsFEM is to approximate the solution…
This paper considers flow problems in multiscale heterogeneous porous media. The multiscale nature of the modeled process significantly complicates numerical simulations due to the need to compute huge and ill-conditioned sparse matrices,…
The purpose of this work is to investigate the behavior of Multiscale Finite Element type methods for advection-diffusion problems in the advection-dominated regime. We present, study and compare various options to address the issue of the…
Complex processes in perforated domains occur in many real-world applications. These problems are typically characterized by physical processes in domains with multiple scales (see Figure 1 for the illustration of a perforated domain).…
Deformable fractured porous media appear in many geoscience applications. While the extended finite element (XFEM) has been successfully developed within the computational mechanics community for accurate modeling of the deformation, its…