Multiscale Finite Element Methods for Nonlinear Problems and Their Applications
نویسندگان
چکیده
In this paper we propose a generalization of multiscale finite element methods (MsFEM) to nonlinear problems. We study the convergence of the proposed method for nonlinear elliptic equations and propose an oversampling technique. Numerical examples demonstrate that the oversampling technique greatly reduces the error. The application of MsFEM to porous media flows is considered. Finally, we describe further generalizations of MsFEM to nonlinear time-dependent equations and discuss the convergence of the method for various kinds of heterogeneities.
منابع مشابه
Investigation of Vacancy Defects on the Young’s Modulus of Carbon Nanotube Reinforced Composites in Axial Direction via a Multiscale Modeling Approach
In this article, the influence of various vacancy defects on the Young’s modulus of carbon nanotube (CNT) - reinforcement polymer composite in the axial direction is investigated via a structural model in ANSYS software. Their high strength can be affected by the presence of defects in the nanotubes used as reinforcements in practical nanocomposites. Molecular structural mechanics (MSM)/finite ...
متن کاملMultiscale Analysis of Transverse Cracking in Cross-Ply Laminated Beams Using the Layerwise Theory
A finite element model based on the layerwise theory is developed for the analysis of transverse cracking in cross-ply laminated beams. The numerical model is developed using the layerwise theory of Reddy, and the von Kármán type nonlinear strain field is adopted to accommodate the moderately large rotations of the beam. The finite element beam model is verified by comparing the present numeric...
متن کاملReduced order modeling techniques for numerical homogenization methods applied to linear and nonlinear multiscale problems
The characteristic of effective properties of physical processes in heterogeneous media is a basic modeling and computational problem for many applications. As standard numerical discretization of such multiscale problems (e.g. with classical finite element method (FEM)) is often computationally prohibitive, there is a need for a novel computational algorithm able to capture the effective behav...
متن کاملMini-Workshop: Numerical Upscaling for Flow Problems: Theory and Applications
The objective of this workshop was to bring together researchers working in multiscale simulations with emphasis on multigrid methods and multiscale finite element methods, aiming at chieving of better understanding and synergy between these methods. The goal of multiscale finite element methods, as upscaling methods, is to compute coarse scale solutions of the underlying equations as accuratel...
متن کاملMultiscale finite element methods for porous media flows and their applications
In this paper, we discuss some applications of multiscale finite element methods to two-phase immiscible flow simulations in heterogeneous porous media. We discuss some extensions of multiscale finite element methods which take into account some limited global information. These methods are well suited for channelized porous media, where the long-range effects are important. This is typical for...
متن کامل