Buch, Englisch, Band 18, 455 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 709 g
Theory and Numerical Treatment
Buch, Englisch, Band 18, 455 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 709 g
Reihe: Springer Series in Computational Mathematics
ISBN: 978-3-662-57217-7
Verlag: Springer
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
- Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
- Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
- Mathematik | Informatik Mathematik Mathematik Interdisziplinär Systemtheorie
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
Weitere Infos & Material
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.