Format:
Online-Ressource (XIV, 455 p. 55 illus., 15 illus. in color, online resource)
Edition:
2nd ed. 2017
ISBN:
9783662549612
Series Statement:
Springer Series in Computational Mathematics 18
Content:
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
Content:
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
Note:
Original first edition u.d.T.: Theorie und Numerik elliptischer Differentialgleichungen, B.G. Teubner, Stuttgart 1987
,
Includes bibliographical references and index
Additional Edition:
ISBN 9783662549605
Additional Edition:
Erscheint auch als Druck-Ausgabe Hackbusch, Wolfgang, 1948 - Elliptic differential equations Berlin : Springer, 2017 ISBN 9783662549605
Additional Edition:
ISBN 3662549603
Language:
English
Subjects:
Mathematics
Keywords:
Elliptische Differentialgleichung
;
Numerisches Verfahren
DOI:
10.1007/978-3-662-54961-2
URL:
Volltext
(lizenzpflichtig)
Author information:
Hackbusch, Wolfgang 1948-
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