The aim of this monograph is to describe the main concepts and recent - vances in multiscale ?nite element methods. This monograph is intended for thebroaderaudienceincludingengineers, appliedscientists, andforthosewho are interested in multiscale simulations. The book is intended for graduate students in applied mathematics and those interested in multiscale compu- tions. It combines a practical introduction, numerical results, and analysis of multiscale ?nite element methods. Due to the page limitation, the material has been condensed. Each chapter of the book starts with an introduction...

The International Conference on "Hyperbolic Problems: Theory, Nu merics and Applications" was held in CalTech on March 25-30, 2002. The Hyp2002 conference was the ninth meeting in the bi-annual international se ries which became one of the highest quality and most successful conference series in Applied Mathematics. This series originated in 1986 at Saint-Etienne, with an earlier focus on the theoretical aspects of hyperbolic conservation laws. As computers became more powerful in the late eighties, and as the interplay between new models, theory and modern numerical algorithms has gained...

Multi-Scale Phenomena in Complex Fluids is a collection of lecture notes delivered during the

The International Conference on "Hyperbolic Problems: Theory, Nu merics and Applications" was held in CalTech on March 25-30, 2002. The Hyp2002 conference was the ninth meeting in the bi-annual international se ries which became one of the highest quality and most successful conference series in Applied Mathematics. This series originated in 1986 at Saint-Etienne, with an earlier focus on the theoretical aspects of hyperbolic conservation laws. As computers became more powerful in the late eighties, and as the interplay between new models, theory and modern numerical algorithms has gained...

This monograph is devoted to the study of multiscale model reduction methods from the point of view of multiscale finite element methods.Multiscale numerical methods have become popular tools for modeling processes with multiple scales. These methods allow reducing the degrees of freedom based on local offline computations. Moreover, these methods allow deriving rigorous macroscopic equations for multiscale problems without scale separation and high contrast. Multiscale methods are also used to design efficient solvers.This book offers a combination of analytical and numerical methods...