ENGLISH

Elliptic Differential Equations: Theory and Numerical Treatment

By Wolfgang Hackbusch (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2017
ISBN
978-3-662-54960-5, 978-3-662-54961-2
DOI
10.1007/978-3-662-54961-2
Language
english
Format
PDF
Filesize
5 MB (4838694 bytes)
Series
Springer Series in Computational Mathematics 18
Edition
2
Pages
XIV, 455\465
Time added
2017-06-25 01:07:36
Analysis;Numerical Analysis;Systems TheoryControl;Calculus of Variations and Optimal ControlMathematical and Computational Physics

Description

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.

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