Related papers: Multiscale modeling for contact problem with high-…
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…
In this paper, we propose a local-global multiscale mortar mixed finite element method (MMMFEM) for multiphase transport in heterogeneous media. We consider the two-phase flow system, the pressure equation is solved via the multiscale…
In this paper, we propose a coupled Discrete Empirical Interpolation Method (DEIM) and Generalized Multiscale Finite element method (GMsFEM) to solve nonlinear parabolic equations with application to the Allen-Cahn equation. The Allen-Cahn…
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…
We propose a generalized multiscale finite element method (GMsFEM) based on clustering algorithm to study the elliptic PDEs with random coefficients in the multi-query setting. Our method consists of offline and online stages. In the…
In this paper, we consider multiscale methods for nonlinear elasticity. In particular, we investigate the Generalized Multiscale Finite Element Method (GMsFEM) for a strain-limiting elasticity problem. Being a special case of the naturally…
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…
In this work we address the Multiscale Spectral Generalized Finite Element Method (MS-GFEM) developed in [I. Babu\v{s}ka and R. Lipton, Multiscale Modeling and Simulation 9 (2011), pp. 373--406]. We outline the numerical implementation of…
The Biot problem of poroelasticity is extended by Signorini contact conditions. The resulting Biot contact problem is formulated and analyzed as a two field variational inequality problem of a perturbed saddle point structure. We present an…
Simulation in media with multiple continua where each continuum interacts with every other is often challenging due to multiple scales and high contrast. One needs some types of model reduction. One of the approaches is multi-continuum…
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…
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…
We introduce a new framework of numerical multiscale methods for advection-dominated problems motivated by climate sciences. Current numerical multiscale methods (MsFEM) work well on stationary elliptic problems but have difficulties when…
We present a multiscale finite element method for a diffusion problem with rough and high contrast coefficients. The construction of the multiscale finite element space is based on the localized orthogonal decomposition methodology and it…
Numerical modeling of wave propagation in heterogeneous media is important in many applications. Due to the complex nature, direct numerical simulations on the fine grid are prohibitively expensive. It is therefore important to develop…
Mortar methods are widely used techniques for discretizations of partial differential equations and preconditioners for the algebraic systems resulting from the discretizations. For problems with high contrast and multiple scales, the…
In this paper, we propose a Bayesian approach for multiscale problems with the availability of dynamic observational data. Our method selects important degrees of freedom probabilistically in a Generalized multiscale finite element method…
In this paper, we propose a space-time GMsFEM for transport equations. Multiscale transport equations occur in many geoscientific applications, which include subsurface transport, atmospheric pollution transport, and so on. Most of existing…
The computational modeling of many engineering problems using the Finite Element method involves the modeling of two or more bodies that meet through an interface. The interface can be physical, as in multi-physics and contact problems, or…
In this paper we develop two goal-oriented adaptive strategies for a posteriori error estimation within the generalized multiscale finite element framework. In this methodology, one seeks to determine the number of multiscale basis…