Elliptic Differential Equations

Theory and Numerical Treatment

Wolfgang Hackbusch

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English

Springer-Verlag Berlin and Heidelberg GmbH & Co. K
12 June 2017

Cybernetics & systems theory; Differential calculus & equations; Calculus of variations; Numerical analysis

Series: Springer Series in Computational Mathematics

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.

By: Wolfgang Hackbusch
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Country of Publication: Germany
Edition: 2nd ed. 2017
Volume: 18
Dimensions: Height: 235mm, Width: 155mm,
Weight: 8.276kg
ISBN: 9783662549605
ISBN 10: 3662549603
Series: Springer Series in Computational Mathematics
Pages: 455
Publication Date: 12 June 2017
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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"".