The aim of this monograph is to describe the main concepts and recent-vances in
multiscale? nite element methods. This monograph is intended for …

Methods for the numerical simulation of dynamic mathematical models have been the focus
of intensive research for well over 60 years. However, rather than reaching closure, there is …

River basin modeling under complexity requires analytical frameworks capable of dealing
with the multiple scales and dimensions of environmental problems as well as uncertainty in …

Simulating electromagnetic fields in the quasi-static regime by solving Maxwell's equations
is a central task in many geophysical applications. In most cases, geophysical targets of …

We consider heterogeneous media whose properties vary in space and particularly aquifers
whose hydraulic conductivity K may change by orders of magnitude in the same formation …

We describe a multilevel multiscale mimetic (M3) method for solving two-phase flow (water
and oil) in a heterogeneous reservoir. The governing equations are the elliptic equation for …

In this paper, we propose a novel nonstandard local Fourier analysis (LFA) variant for
accurately predicting the multigrid convergence of problems with random and jumping …

An important issue in the numerical simulation of geothermal reservoirs is the problem of
scales. Data are collected at a scale usually smaller than the one used to discretise the …

We consider a second order elliptic problem with a heterogeneous coefficient written in
mixed form. The nonoverlapping mortar domain decomposition method is efficient in parallel …

This contribution presents a comprehensive, in-depth analysis of the solution of the
mechanical equilibrium problem for a generic solid with microstructure. The exact solution to …