Author	Hackbusch, Wolfgang. author
Title	Elliptic Differential Equations [electronic resource] : Theory and Numerical Treatment / by Wolfgang Hackbusch
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2017
Edition	2nd ed. 2017
Connect to	http://dx.doi.org/10.1007/978-3-662-54961-2
Descript	XIV, 455 p. 55 illus., 15 illus. in color. online resource

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

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

1. Mathematics
2. Mathematical analysis
3. Analysis (Mathematics)
4. System theory
5. Numerical analysis
6. Calculus of variations
7. Physics
8. Mathematics
9. Analysis
10. Numerical Analysis
11. Systems Theory
12. Control
13. Calculus of Variations and Optimal Control; Optimization
14. Theoretical
15. Mathematical and Computational Physics