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Elliptic Differential Equations [electronic resource] : Theory and Numerical Treatment / by Wolfgang Hackbusch.

By: Hackbusch, Wolfgang [author.].
Contributor(s): SpringerLink (Online service).
Material type: TextTextSeries: Springer Series in Computational Mathematics: 18Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2017Edition: 2nd ed. 2017.Description: XIV, 455 p. 55 illus., 15 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783662549612.Subject(s): Global analysis (Mathematics) | Numerical analysis | Systems theory | Mathematical optimization | Analysis | Numerical Analysis | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Theoretical, Mathematical and Computational PhysicsAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 515 Online resources: Click here to access online
Contents:
1 Partial Differential Equations and Their Classification Into Types -- 2 The Potential Equation -- 3 The Poisson Equation -- 4 Difference Methods for the Poisson Equation -- 5 General Boundary Value Problems -- 6 Tools from Functional Analysis -- 7 Variational Formulation -- 8 The Method of Finite Elements -- 9 Regularity -- 10 Special Differential Equations -- 11 Eigenvalue Problems -- 12 Stokes Equations.
In: Springer eBooksSummary: 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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E-BOOKS E-BOOKS ISI Library, Kolkata
 
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1 Partial Differential Equations and Their Classification Into Types -- 2 The Potential Equation -- 3 The Poisson Equation -- 4 Difference Methods for the Poisson Equation -- 5 General Boundary Value Problems -- 6 Tools from Functional Analysis -- 7 Variational Formulation -- 8 The Method of Finite Elements -- 9 Regularity -- 10 Special Differential Equations -- 11 Eigenvalue Problems -- 12 Stokes Equations.

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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