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Numerical Models for Differential Problems

  • Textbook
  • © 2014

Overview

Authors:
  1. Alfio Quarteroni

    1. CMCS-MATHICSE, Ecole Polytechnique Fédérale de Lausanne, Switzerland
      MOX, Department of Mathematics “F. Brioschi”, Politecnico di Milano, Italy

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  • Author faces here the basic concepts for the numerical modeling of partial differential equations
  • An outstanding reference work in this branch of applied mathematics
  • In particular, the author discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs
  • Includes supplementary material: sn.pub/extras

Part of the book series: MS&A (MS&A, volume 8)

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Table of contents (19 chapters)

  1. Front Matter

    Pages I-XIX
    Download chapter PDF

  2. A brief survey of partial differential equations

    • Alfio Quarteroni
    Pages 1-10

  3. Elements of functional analysis

    • Alfio Quarteroni
    Pages 11-29

  4. Elliptic equations

    • Alfio Quarteroni
    Pages 31-60

  5. The Galerkin finite element method for elliptic problems

    • Alfio Quarteroni
    Pages 61-119

  6. Parabolic equations

    • Alfio Quarteroni
    Pages 121-140

  7. Generation of 1D and 2D grids

    • Alfio Quarteroni
    Pages 141-159

  8. Algorithms for the solution of linear systems

    • Alfio Quarteroni
    Pages 161-177

  9. Elements of finite element programming

    • Alfio Quarteroni
    Pages 179-212

  10. The finite volume method

    • Alfio Quarteroni
    Pages 213-223

  11. Spectral methods

    • Alfio Quarteroni
    Pages 225-266

  12. Discontinuous element methods (DG and mortar)

    • Alfio Quarteroni
    Pages 267-289

  13. Diffusion-transport-reaction equations

    • Alfio Quarteroni
    Pages 291-338

  14. Finite differences for hyperbolic equations

    • Alfio Quarteroni
    Pages 339-370

  15. Finite elements and spectral methods for hyperbolic equations

    • Alfio Quarteroni
    Pages 371-408

  16. Nonlinear hyperbolic problems

    • Alfio Quarteroni
    Pages 409-428

  17. Navier-Stokes equations

    • Alfio Quarteroni
    Pages 429-482

  18. Optimal control of partial differential equations

    • Alfio Quarteroni
    Pages 483-525

  19. Domain decomposition methods

    • Alfio Quarteroni
    Pages 527-584

  20. Reduced basis approximation for parametrized partial differential equations

    • Alfio Quarteroni
    Pages 585-633
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Keywords

About this book

In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.

Authors and Affiliations

  • CMCS-MATHICSE, Ecole Polytechnique Fédérale de Lausanne, Switzerland

    Alfio Quarteroni

  • MOX, Department of Mathematics “F. Brioschi”, Politecnico di Milano, Italy

    Alfio Quarteroni

About the author

The Author is Professor and Director of the Chair of Modelling and Scientific Computing (CMCS) at the Institute of Analysis and Scientific Computing of EPFL, Lausanne (Switzerland), since 1998, Professor of Numerical Analysis at the Politecnico di Milano (Italy) since 1989, and Scientific Director of MOX, since 2002. Author of 22 books published with Springer, and of about 200 papers published in refereed international Journals, Conference Proceedings and Magazines, Alfio Quarteroni is actually one of the strongest and reliable mathematicians in the world in the field of Modelling and SC.

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