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Finite Difference Methods on Irregular Networks

BuchGebunden
206 Seiten
Englisch
Springererschienen am01.01.1987
The finite difference and finite element methods are powerful tools for the approximate solution of differential equations governing diverse physical phenomena, and there is extensive literature on these discre­ tization methods.mehr
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EUR85,55
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Produkt

KlappentextThe finite difference and finite element methods are powerful tools for the approximate solution of differential equations governing diverse physical phenomena, and there is extensive literature on these discre­ tization methods.
Details
ISBN/GTIN978-3-7643-1880-2
ProduktartBuch
EinbandartGebunden
Verlag
Erscheinungsjahr1987
Erscheinungsdatum01.01.1987
ReiheInternational Series of Numerical Mathematics .82
Reihen-Nr..82
Seiten206 Seiten
SpracheEnglisch
Gewicht440 g
Illustrationen206 p.
Artikel-Nr.16080443

Inhalt/Kritik

Inhaltsverzeichnis
1. Introduction.- 1.1. Preliminary remarks.- 1.2. Scope of monograph.- 1.3. Plan of monograph, comments.- 2. Boundary Value Problems and Irregular Networks.- 2.1. A class of elliptic problems.- 2.2. Irregular networks.- 2.3. Secondary networks and boxes.- 3. Construction of Finite Difference Approximations.- 3.1. The principle of approximation.- 3.2. Finite difference schemes via method (PB).- 3.3. Finite difference schemes via method (MD).- 4. Analytical and Matrix Properties of the Difference Operators Ah.- 4.1. General remarks and notations.- 4.2. Monotonicity and other matrix properties.- 4.3. Scalar products, norms and a trace theorem.- 4.4. Green´s formula, inequalities of Friedrichs-Poincaré- type and the positive definiteness of Ah.- 4.5. A priori estimates for Ah using the W12- and C-norm.- 5. Error Estimates and Convergence.- 5.1. Error splitting and approaches to the error estimation.- 5.2. The error æ of the principal part of PB-operators.- 5.3. The error æ of the principal part of MD-operators.- 5.4. The error ?N for PB- MD-schemes.- 5.5. Convergence for W22(?)-solutions.- 6. Finite Difference Schemes for Nonsymmetric Problems.- 6.1. Construction of finite difference approximations.- 6.2. Properties of the difference operators $${\text{A}}_{{\text{h}}}^{{\text{b}}}$$.- 6.3. The error convection term.- 7. Concluding Remarks.- Appendices.- 1. Appendix DI: Relations of Differential and Integral calculus, norms.- 2. Appendix ES: Estimation of functionals on Sobolev spaces.- 3. Appendix EX: Extension of functions.- 4. Appendix GE: Some relations of geometry.- 5. Appendix IM: Imbedding and trace theorems.- 6. Appendix TR: Affine transformations of coordinates and functional.- References.- List of Figures.- Abbreviations.- Notations.mehr