In this paper, we discuss a general multiscale model reduction framework based on
multiscale finite element methods. We give a brief overview of related multiscale methods …

The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modeling and the …

In this paper, we discuss the application of generalized multiscale finite element method
(GMsFEM) to elasticity equation in heterogeneous media. We consider steady state elasticity …

This paper presents HDGlab, an open source MATLAB implementation of the hybridisable
discontinuous Galerkin (HDG) method. The main goal is to provide a detailed description of …

A condensed algorithm for adaptive component mode synthesis is proposed to compute the
dynamics of viscoelastic flexible multibody systems efficiently and accurately. As studied, the …

This monograph requires basic knowledge of the variational theory of elliptic PDE and the
techniques used for the analysis of the Finite Element Method. However, all the tools for the …

Abstract We devise a Hybrid High-Order (HHO) method for highly oscillatory elliptic
problems that is capable of handling general meshes. The method hinges on discrete …

The multiscale hybrid-mixed (MHM) method is extended to the Stokes and Brinkman
equations with highly heterogeneous coefficients. The approach is constructive. We first …

We discuss three-dimensional suspension-colloidal-nano transport in anisotropic porous
media. The Boltzmann kinetic equation captures stochastic particle velocity distribution on …

Mortar methods are widely used techniques for discretizations of partial differential
equations and preconditioners for the algebraic systems resulting from the discretizations …