Related papers: A multiscale method for inhomogeneous elastic prob…

In this paper, we present two adaptive methods for the basis enrichment of the mixed Generalized Multiscale Finite Element Method (GMsFEM) for solving the flow problem in heterogeneous media. We develop an a-posteriori error indicator which…

In this paper, we develop a multiscale finite element method for solving flows in fractured media. Our approach is based on Generalized Multiscale Finite Element Method (GMsFEM), where we represent the fracture effects on a coarse grid via…

Finite differences, finite elements, and their generalizations are widely used for solving partial differential equations, and their high-order variants have respective advantages and disadvantages. Traditionally, these methods are treated…

A novel multi-scale finite element formulation for contact mechanics between nominally smooth but microscopically rough surfaces is herein proposed. The approach integrates the interface finite element method (FEM) for modelling interface…

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…

We present a method of CutFEM type for the Poisson problem with either Dirichlet or Neumann boundary conditions. The computational mesh is obtained from a background (typically uniform Cartesian) mesh by retaining only the elements…

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…

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…

The conformal formulation of the Einstein constraint equations is first reviewed, and we then consider the design, analysis, and implementation of adaptive multilevel finite element-type numerical methods for the resulting coupled nonlinear…

The Heterogeneous Multiscale Finite Element Method (FE-HMM) is a two-scale FEM based on asymptotic homogenization for solving multiscale partial differential equations. It was introduced in [W. E and B. Engquist, \emph{Commun. Math. Sci.},…

Simulating complex processes in fractured media requires some type of model reduction. Well-known approaches include multi-continuum techniques, which have been commonly used in approximating subgrid effects for flow and transport in…

We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…

In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. Mixed generalized multiscale finite element method (GMsFEM)…

In this paper, we discuss the application of the Generalized Finite Element Method (GFEM) to approximate the solutions of quasilinear elliptic equations with multiple interfaces in one dimensional space. The problem is characterized by…

This paper is devoted to the study of a novel mixed Finite Element Method for approximating the solutions of fourth order variational problems subjected to a constraint. The first problem we consider consists in establishing the convergence…

We study the numerical approximation of advection-diffusion equations with highly oscillatory coefficients and possibly dominant advection terms by means of the Multiscale Finite Element Method. The latter method is a now classical, finite…

We define a new finite element method for a steady state elliptic problem with discontinuous diffusion coefficients where the meshes are not aligned with the interface. We prove optimal error estimates in the $L^2$ norm and $H^1$ weighted…

We develop a new multiscale finite element method for Laplace equation with oscillating Neumann boundary conditions on rough boundaries. The key point is the introduction of a new boundary condition that incorporates both the…

A surface integral representation of Maxwell's equations allows the efficient electromagnetic (EM) modeling of three-dimensional structures with a two-dimensional discretization, via the boundary element method (BEM). However, existing BEM…

Cosserat theory of elasticity is a generalization of classical elasticity that allows for asymmetry in the stress tensor by taking into account micropolar rotations in the medium. The equations involve a rotation field and associated…