Elliptic Differential Equations: Theory and Numerical Treatment (Springer Series in Computational Mechanics)

Hackbusch, W., Fadiman, Regine, Ion, Patrick D. F.

ISBN 10: 038754822X / ISBN 13: 9780387548227

Published by Springer Nature, 1992

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Bibliographic Details

• Title: Elliptic Differential Equations: Theory and Numerical Treatment (Springer Series in Computational Mechanics)
• Publisher: Springer Nature
• Publication Date: 1992
• Language: English
• ISBN 10: 038754822X
• ISBN 13: 9780387548227
• Binding: Hardcover
• Condition: Like New
• Book Type: book

About this title

Synopsis

The book offers a simultaneous presentation of the theory and of the numerical treatment of elliptic problems. The author starts with a discussion of the Laplace equation in the classical formulation and its discretisation by finite differences and deals with topics of gradually increasing complexity in the following chapters. He introduces the variational formulation of boundary value problems together with the necessary background from functional analysis and describes the finite element method including the most important error estimates. A more advanced chapter leads the reader into the theory of regularity. The reader will also find more details about the discretisation of singularly perturbed equations and eigenvalue problems. The author discusses the Stokes problem as an example of a saddle point problem taking into account its relevance to applications in fluid dynamics.

From the Back Cover

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.