E-Book, Englisch, 364 Seiten
Thomee Galerkin Finite Element Methods for Parabolic Problems
2. Auflage 2007
ISBN: 978-3-540-33122-3
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
E-Book, Englisch, 364 Seiten
ISBN: 978-3-540-33122-3
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
This book provides insight into the mathematics of Galerkin finite element method as applied to parabolic equations. The revised second edition has been influenced by recent progress in application of semigroup theory to stability and error analysis, particulatly in maximum-norm. Two new chapters have also been added, dealing with problems in polygonal, particularly noncovex, spatial domains, and with time discretization based on using Laplace transformation and quadrature.
Autoren/Hrsg.
Weitere Infos & Material
1;Preface;5
2;Preface to the Second Edition;9
3;Table of Contents;11
4;1. The Standard Galerkin Method;13
5;2. Methods Based on More General Approximations of the Elliptic Problem;37
6;3. Nonsmooth Data Error Estimates;48
7;4. More General Parabolic Equations;66
8;5. Negative Norm Estimates and Superconvergence;78
9;6. Maximum-Norm Estimates and Analytic Semigroups;92
10;7. Single Step Fully Discrete Schemes for the Homogeneous Equation;121
11;8. Single Step Fully Discrete Schemes for the Inhomogeneous Equation;138
12;9. Single Step Methods and Rational Approximations of Semigroups;157
13;10. Multistep Backward Difference Methods;170
14;11. Incomplete Iterative Solution of the Algebraic Systems at the Time Levels;192
15;12. The Discontinuous Galerkin Time Stepping Method;210
16;13. A Nonlinear Problem;238
17;14. Semilinear Parabolic Equations;252
18;15. The Method of Lumped Masses;268
19;16. The H1 and H- Methods;286
20;17. A Mixed Method;300
21;18. A Singular Problem;312
22;19. Problems in Polygonal Domains;323
23;20. Time Discretization by Laplace Transformation and Quadrature;341
24;References;361
25;Index;375
