# Numerical Approximation of Partial Differential Equations

Book

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

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

1. Pages 1-16
2. Pages 17-71
3. Pages 73-100
4. Pages 101-127
5. Pages 129-157
3. ### Approximation of Boundary Value Problems

1. Pages 257-296
2. Pages 297-337
3. Pages 339-362
4. ### Approximation of Initial-Boundary Value Problems

1. Pages 363-404
2. Pages 405-427
3. Pages 429-448
4. Pages 449-508
5. Back Matter
Pages 509-543

### 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

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

• Book Title Numerical Approximation of Partial Differential Equations
• Authors Alfio Quarteroni
Alberto Valli
• Series Title Springer Series in Computational Mathematics
• DOI https://doi.org/10.1007/978-3-540-85268-1
• Copyright Information Springer Berlin Heidelberg 1994
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Hardcover ISBN 978-3-540-57111-7
• Softcover ISBN 978-3-540-85267-4
• eBook ISBN 978-3-540-85268-1
• Series ISSN 0179-3632
• Edition Number 1
• Number of Pages XVI, 544
• Number of Illustrations 59 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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