Elliptic Differential Equations | Buch

Cover: 9783662549605 | Elliptic Differential Equations | Theory and Numerical Treatment | xiv

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Sprache: Englisch

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Beschreibung

This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite-element methods, which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle-point problem taking into account its relevance to applications in fluid dynamics.

Über den Autor

The author is a very well-known author of Springer, working in the field of numerical mathematics for partial differential equations and integral equations. He has published numerous books in the SSCM series, e.g., about the multi-grid method, about the numerical analysis of elliptic pdes, about iterative solution of large systems of equation, and a book in German about the technique of hierarchical matrices. Hackbusch is member of the editorial board of Springer' s book series "Advances in Numerical Mathematics", "The International Cryogenics Monograph Series" and "Springer Series of Computational Mathematics".

Zusammenfassung

Provides a detailed analysis of both the continuous boundary value problems and the discretisation methods

Includes numerous exercises for readers to test their understanding of the text

Discusses in detail the topics regularity of the solution of a boundary value problem and eigenvalue problems

Inhaltsverzeichnis

1 Partial Differential Equations and Their Classification Into Types.- 2 The Potential Equation.- 3 The Poisson Equation.- 4 Difference Methods for the Poisson Equation.- 5 General Boundary Value Problems.- 6 Tools from Functional Analysis.- 7 Variational Formulation.- 8 The Method of Finite Elements.- 9 Regularity.- 10 Special Differential Equations.- 11 Eigenvalue Problems.- 12 Stokes Equations.

Erscheinungsjahr:	2017
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Springer Series in Computational Mathematics
Inhalt:	xiv 455 S. 40 s/w Illustr. 15 farbige Illustr. 455 p. 55 illus. 15 illus. in color.
ISBN-13:	9783662549605
ISBN-10:	3662549603
Sprache:	Englisch
Herstellernummer:	978-3-662-54960-5
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Hackbusch, Wolfgang
Auflage:	2nd ed. 2017
Hersteller:	Springer-Verlag GmbH Springer Berlin Heidelberg Springer Series in Computational Mathematics
Maße:	241 x 160 x 31 mm
Von/Mit:	Wolfgang Hackbusch
Erscheinungsdatum:	12.06.2017
Gewicht:	0,869 kg

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