Numerical Approximation of Partial Differential Equations

  • Alfio Quarteroni
  • Alberto Valli

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 23)

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Basic Concepts and Methods for PDEs’ Approximation

  3. Approximation of Boundary Value Problems

  4. Approximation of Initial-Boundary Value Problems

  5. Back Matter
    Pages 509-543

About this book

Introduction

This book deals with the numerical approximation of partial differential equations. Its scope is to provide a thorough illustration of numerical methods, carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is one of its main features. Many kinds of problems are addressed. A comprehensive theory of Galerkin method and its variants, as well as that of collocation methods, are developed for the spatial discretization. These theories are then specified to two numerical subspace realizations of remarkable interest: the finite element method and the spectral method. 

From the reviews:

"...The book is excellent and is addressed to post-graduate students, research workers in applied sciences as well as to specialists in numerical mathematics solving PDE. Since it is written very clearly, it would be acceptable for undergraduate students in advanced courses of numerical mathematics. Readers will find this book to be a great pleasure."--MATHEMATICAL REVIEWS

 

Keywords

Algorithmen Approximation Numerische Approximation algorithm algorithms differential equation finite Elemente finite element method finite elements numerical methods partial differential equation partial differential equations partielle Differentialgleichung partielle Differentialgleichungen spektral Methoden

Authors and affiliations

  • Alfio Quarteroni
    • 1
    • 2
  • Alberto Valli
    • 3
  1. 1.École Polytechnique Fédérale de Lausanne Chaire de Modelisation et Calcul Scientifique (CMCS)LausanneSwitzerland
  2. 2.Politecnico di MilanoMOXMilanItaly
  3. 3.Dipartimento di MatematicaUniversità di TrentoPovo TNItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-85268-1
  • Copyright Information Springer Berlin Heidelberg 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-85267-4
  • Online ISBN 978-3-540-85268-1
  • Series Print ISSN 0179-3632
  • About this book