1 option
Elliptic Differential Equations : Theory and Numerical Treatment / by Wolfgang Hackbusch.
Springer Nature - Springer Mathematics and Statistics eBooks 2017 English International Available online
View online- Format:
- Book
- Author/Creator:
- Hackbusch, Wolfgang., Author.
- Series:
- Springer Series in Computational Mathematics, 0179-3632 ; 18
- Language:
- English
- Subjects (All):
- Mathematical analysis.
- Analysis (Mathematics).
- Numerical analysis.
- System theory.
- Calculus of variations.
- Mathematical physics.
- Analysis.
- Numerical Analysis.
- Systems Theory, Control.
- Calculus of Variations and Optimal Control; Optimization.
- Theoretical, Mathematical and Computational Physics.
- Local Subjects:
- Analysis.
- Numerical Analysis.
- Systems Theory, Control.
- Calculus of Variations and Optimal Control; Optimization.
- Theoretical, Mathematical and Computational Physics.
- Physical Description:
- 1 online resource (XIV, 455 p. 55 illus., 15 illus. in color.)
- Edition:
- 2nd ed. 2017.
- Place of Publication:
- Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2017.
- Summary:
- 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.
- 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.
- Notes:
- Includes bibliographical references and index.
- ISBN:
- 3-662-54961-1
The Penn Libraries is committed to describing library materials using current, accurate, and responsible language. If you discover outdated or inaccurate language, please fill out this feedback form to report it and suggest alternative language.