Numerical Models for Differential Problems

  • Alfio Quarteroni

Part of the MS&A book series (MS&A, volume 2)

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

Analysis Numerical modelling PDE algorithms finite element method hyperbolic equation partial differential equation

Authors and affiliations

  • Alfio Quarteroni
    • 1
    • 2
  1. 1.MOX, Department of Mathematics “F. Brioschi”Politecnico di MilanoMilanItaly
  2. 2.CMCS-IACSEcole Polytechnique Fédérale de LausanneLausanneSwitzerland

Bibliographic information

  • DOI https://doi.org/10.1007/978-88-470-1071-0
  • Copyright Information Springer-Verlag Milan 2009
  • Publisher Name Springer, Milano
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-88-470-1070-3
  • Online ISBN 978-88-470-1071-0
  • About this book