Numerical Models for Differential Problems

  • Alfio Quarteroni

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
  17. Back Matter
    Pages 635-658

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.


PDE analysis numerical modelling

Authors and affiliations

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

Bibliographic information