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Elliptic Differential Equations

Theory and Numerical Treatment. Springer Series in Computational Mathematics 18

By (author) Wolfgang Hackbusch
Format: Paperback / softback
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin, Germany
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Published: 12th May 2018
Dimensions: w 156mm h 234mm d 24mm
Weight: 657g
ISBN-10: 3662572176
ISBN-13: 9783662572177
Barcode No: 9783662572177
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Synopsis
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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