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Multiscale and Adaptivity: Modeling, Numerics and Applications

C.I.M.E. Summer School, Cetraro, Italy 2009

  • Book
  • © 2012

Overview

Authors:
  1. Silvia Bertoluzza

    1. Istituto di Matematica Applicata, e Tecnologie Informatiche, CNR, Pavia, Italy

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  2. Ricardo H. Nochetto

    1. Department of Mathematics, University of Maryland, College Park, USA

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  3. Alfio Quarteroni

    1. Chaire de Modelisation, et Calcul Scientifique (CMCS), École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

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  4. Kunibert G. Siebert

    1. Fakultät für Mathematik und Physik, Universität Stuttgart, Stuttgart, Germany

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  5. Andreas Veeser

    1. Dipartimento di Matematica, Università degli Studi di Milano, Milano, Italy

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  • 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
  • Includes supplementary material: sn.pub/extras

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

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xii
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  2. Adaptive Wavelet Methods

    • Silvia Bertoluzza
    Pages 1-56

  3. Heterogeneous Mathematical Models in Fluid Dynamics and Associated Solution Algorithms

    • Marco Discacciati, Paola Gervasio, Alfio Quarteroni
    Pages 57-123

  4. Primer of Adaptive Finite Element Methods

    • Ricardo H. Nochetto, Andreas Veeser
    Pages 125-225

  5. Mathematically Founded Design of Adaptive Finite Element Software

    • Kunibert G. Siebert
    Pages 227-309

  6. Back Matter

    Pages 311-314
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Keywords

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.

Authors and Affiliations

  • Istituto di Matematica Applicata, e Tecnologie Informatiche, CNR, Pavia, Italy

    Silvia Bertoluzza

  • Department of Mathematics, University of Maryland, College Park, USA

    Ricardo H. Nochetto

  • Chaire de Modelisation, et Calcul Scientifique (CMCS), École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Alfio Quarteroni

  • Fakultät für Mathematik und Physik, Universität Stuttgart, Stuttgart, Germany

    Kunibert G. Siebert

  • Dipartimento di Matematica, Università degli Studi di Milano, Milano, Italy

    Andreas Veeser

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