相关论文: Corrector theory for MsFEM and HMM in random media

This paper analyzes the random fluctuations obtained by a heterogeneous multi-scale first-order finite element method applied to solve elliptic equations with a random potential. We show that the random fluctuations of such solutions are…

How heterogeneous multiscale methods (HMM) handle fluctuations acting on the slow variables in fast-slow systems is investigated. In particular, it is shown via analysis of central limit theorems (CLT) and large deviation principles (LDP)…

This paper concerns the analysis of a multiscale method for wave propagation problems in microscopically nonhomogeneous media. A direct numerical approximation of such problems is prohibitively expensive as it requires resolving the…

In this paper, we suggest a new heterogeneous multiscale method (HMM) for the time-harmonic Maxwell equations in locally periodic media. The method is constructed by using a divergence-regularization in one of the cell problems. This allows…

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…

Stochastic modeling has become a popular approach to quantify uncertainty in flows through heterogeneous porous media. The uncertainty in heterogeneous structure properties is often parameterized by a high-dimensional random variable. This…

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…

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.},…

In this paper, we provide the constraint energy minimization generalized multiscale finite element method (CEM-GMsFEM) to solve Helmholtz equations in heterogeneous medium. This novel multiscale method is specifically designed to overcome…

This paper presents a high-accuracy higher-order multiscale method for solving multi-continuum problems in in highly heterogeneous media. First, microscopic unit cell functions are defined, leading to the derivation of macroscopic…

In this paper, we address the numerical homogenization approximation of a free-boundary dam problem posed in a heterogeneous media. More precisely, we propose a generalized multiscale finite element (GMsFEM) method for the heterogeneous dam…

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 Hessian discretisation method (HDM) for fourth order linear elliptic equations provides a unified convergence analysis framework based on three properties namely coercivity, consistency, and limit-conformity. Some examples that fit in…

We study the stochastic homogenization and obtain a random fluctuation theory for semilinear elliptic equations with a rapidly varying random potential. To first order, the effective potential is the average potential and the nonlinearity…

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…

In this paper, we suggest a new Heterogeneous Multiscale Method (HMM) for the Helmholtz equation with high contrast. The method is constructed for a setting as in Bouchitt\'e and Felbacq (C.R. Math. Acad. Sci. Paris 339(5):377--382, 2004),…

This work is devoted to the asymptotic behavior of eigenvalues of an elliptic operator with rapidly oscillating random coefficients on a bounded domain with Dirichlet boundary conditions. A sharp convergence rate is obtained for isolated…

This paper presents a homogenization framework for elastomeric metamaterials exhibiting long-range correlated fluctuation fields. Based on full-scale numerical simulations on a class of such materials, an ansatz is proposed that allows to…

This paper deals with the homogenization problem of one-dimensional pseudo-elliptic equations with a rapidly varying random potential. The main purpose is to characterize the homogenization error (random fluctuations), i.e., the difference…

We propose a stochastic multiscale finite element method (StoMsFEM) to solve random elliptic partial differential equations with a high stochastic dimension. The key idea is to simultaneously upscale the stochastic solutions in the physical…