Overview
- 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
Part of the book series: Springer Series in Computational Mathematics (SSCM, volume 18)
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Elliptic Differential Equations
Book Subtitle: Theory and Numerical Treatment
Authors: Wolfgang Hackbusch
Series Title: Springer Series in Computational Mathematics
DOI: https://doi.org/10.1007/978-3-662-54961-2
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag GmbH Germany 2017
Hardcover ISBN: 978-3-662-54960-5Published: 12 June 2017
Softcover ISBN: 978-3-662-57217-7Published: 12 May 2018
eBook ISBN: 978-3-662-54961-2Published: 01 June 2017
Series ISSN: 0179-3632
Series E-ISSN: 2198-3712
Edition Number: 2
Number of Pages: XIV, 455
Number of Illustrations: 40 b/w illustrations, 15 illustrations in colour
Topics: Analysis, Numerical Analysis, Systems Theory, Control, Calculus of Variations and Optimal Control; Optimization, Theoretical, Mathematical and Computational Physics