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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.
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.
Details
| 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 |
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.
Details
| 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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