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Elliptic Differential Equations

by Hackbusch, Wolfgang.
Authors: SpringerLink (Online service) Series: Springer Series in Computational Mathematics, 0179-3632 ; . 18 Published by : Springer Berlin Heidelberg, (Berlin, Heidelberg :) Physical details: XIV, 311p. 40 illus. digital. ISBN: 3642114903 Subject(s): Mathematics. | Global analysis (Mathematics). | Systems theory. | Numerical analysis. | Mathematical optimization. | Mathematics. | Analysis. | Numerical Analysis. | Systems Theory, Control. | Calculus of Variations and Optimal Control; Optimization. | Theoretical, Mathematical and Computational Physics. Year: 2010
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E-Book E-Book AUM Main Library 515 (Browse Shelf) Not for loan

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.

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