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© 2014

Numerical Models for Differential Problems

Textbook

Part of the MS&A - Modeling, Simulation and Applications book series (MS&A, volume 8)

Table of contents

  1. Front Matter
    Pages I-XIX
  2. Alfio Quarteroni
    Pages 11-29
  3. Alfio Quarteroni
    Pages 31-60
  4. Alfio Quarteroni
    Pages 121-140
  5. Alfio Quarteroni
    Pages 141-159
  6. Alfio Quarteroni
    Pages 161-177
  7. Alfio Quarteroni
    Pages 179-212
  8. Alfio Quarteroni
    Pages 213-223
  9. Alfio Quarteroni
    Pages 225-266
  10. Alfio Quarteroni
    Pages 267-289
  11. Alfio Quarteroni
    Pages 291-338
  12. Alfio Quarteroni
    Pages 339-370
  13. Alfio Quarteroni
    Pages 409-428
  14. Alfio Quarteroni
    Pages 429-482
  15. Alfio Quarteroni
    Pages 483-525
  16. Alfio Quarteroni
    Pages 527-584

About this book

Introduction

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.

Keywords

PDE analysis numerical modelling

Authors and affiliations

  1. 1.CMCS-MATHICSEEcole Polytechnique Fédérale de LausanneSwitzerland
  2. 2.MOX, Department of Mathematics “F. Brioschi”Politecnico di MilanoItaly

About the authors

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.

Bibliographic information