© 2012

Multiscale and Adaptivity: Modeling, Numerics and Applications

C.I.M.E. Summer School, Cetraro, Italy 2009, Editors: Giovanni Naldi, Giovanni Russo

  • Gives an overview of state-of-the-art mathematical tools in multiscale modeling

  • Contains a chapter on multiscale modeling and related numerical methods in fluid dynamics

  • Provides a detailed description of adaptive finite element methods, ranging from the mathematical theory to implementation details and software development


Part of the Lecture Notes in Mathematics book series (LNM, volume 2040)

Also part of the C.I.M.E. Foundation Subseries book sub series (LNMCIME, volume 2040)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Silvia Bertoluzza
    Pages 1-56
  3. Marco Discacciati, Paola Gervasio, Alfio Quarteroni
    Pages 57-123
  4. Ricardo H. Nochetto, Andreas Veeser
    Pages 125-225
  5. Back Matter
    Pages 311-314

About this book


This book is a collection of lecture notes for the CIME course on "Multiscale and Adaptivity: Modeling, Numerics and Applications," held in Cetraro (Italy), in July 2009.
Complex systems arise in several physical, chemical, and biological processes, in which length and time scales may span several orders of magnitude. Traditionally, scientists have focused on methods that are particularly applicable in only one regime, and knowledge of the system on one scale has been transferred to another scale only indirectly. 
Even with modern computer power, the complexity of such systems precludes their being treated directly with traditional tools, and new mathematical and computational instruments have had to be developed to tackle such problems.  The outstanding and internationally renowned lecturers, coming from different areas of Applied Mathematics, have themselves contributed in an essential way to the development of the theory and techniques that constituted the subjects of the courses.


65M50, 65N50, 65M55, 65T60, 65N30, 65M60, 76MXX 65M50, 65N50, 65M55, 65T60, 65N30, 76MXX adaptive finite elements heterogeneous models in fluid dynamics multiscale modeling and simulation wavelets

Authors and affiliations

  1. 1.Istituto di Matematica Applicata, e Tecnologie InformaticheCNRPaviaItaly
  2. 2.Department of MathematicsUniversity of MarylandCollege ParkUSA
  3. 3.Chaire de Modelisation, et Calcul Scientifique (CMCS)École Polytechnique Fédérale de LausanneLausanneSwitzerland
  4. 4.Fakultät für Mathematik und PhysikUniversität StuttgartStuttgartGermany
  5. 5.Dipartimento di MatematicaUniversità degli Studi di MilanoMilanoItaly

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