Elliptic Differential Equations

Theory and Numerical Treatment

By:

Wolfgang Hackbusch

Format:

Paperback / softback

Series:

Springer Series in Computational Mathematics

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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.

Author Biography:

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".

Release date Australia

May 12th, 2018

Author

Wolfgang Hackbusch

Series

Springer Series in Computational Mathematics

Pages

455

Edition

Softcover reprint of the original 2nd ed. 2017

Audience

Professional & Vocational

Illustrations

15 Illustrations, color; 40 Illustrations, black and white; XIV, 455 p. 55 illus., 15 illus. in color.

ISBN-13

9783662572177

Product ID

28359936

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