Numerical Models for Differential Problems

  • Alfio¬†Quarteroni

Part of the MS&A book series (MS&A, volume 16)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Alfio Quarteroni
    Pages 11-29
  3. Alfio Quarteroni
    Pages 31-59
  4. Alfio Quarteroni
    Pages 121-140
  5. Alfio Quarteroni
    Pages 141-160
  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 267-292
  11. Alfio Quarteroni
    Pages 293-314
  12. Alfio Quarteroni
    Pages 315-365
  13. Alfio Quarteroni
    Pages 367-398
  14. Alfio Quarteroni
    Pages 437-455
  15. Alfio Quarteroni
    Pages 457-510
  16. Alfio Quarteroni
    Pages 511-553
  17. Alfio Quarteroni
    Pages 555-612

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 numerical analysis computational mathematics applications of mathematics

Authors and affiliations

  • Alfio¬†Quarteroni
    • 1
  1. 1.Politecnico di MilanoMilanItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-49316-9
  • Copyright Information Springer International Publishing, AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-49315-2
  • Online ISBN 978-3-319-49316-9
  • Series Print ISSN 2037-5255
  • Series Online ISSN 2037-5263
  • About this book