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Elliptic Differential Equations: Theory and Numerical Treatment: 18 (Springer Series in Computational Mathematics) - Hardcover
Inhaltsangabe
<P>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.</P>
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Reseña del editor
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.
Biografía del 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".
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- VerlagSpringer
- Erscheinungsdatum2017
- ISBN 10 3662549603
- ISBN 13 9783662549605
- EinbandTapa dura
- SpracheEnglisch
- Auflage2
- Anzahl der Seiten472
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Elliptic Differential Equations: Theory and Numerical Treatment (Springer Series in Computational Mathematics, 18)
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Elliptic Differential Equations : Theory and Numerical Treatment
Verlag:
Springer Berlin Heidelberg, Springer Berlin Heidelberg, 2017
ISBN 10: 3662549603
ISBN 13: 9783662549605
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Hardcover
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Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Artikel-Nr. 9783662549605
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Elliptic Differential Equations: Theory and Numerical Treatment
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Hardcover. Zustand: Brand New. 2nd edition. 455 pages. 9.25x6.25x1.25 inches. In Stock. Artikel-Nr. x-3662549603
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