《抛物问题的伽辽金有限元方法第2版》由瑞典托姆著，主要内容：The
basis of this work is my earlier text entitled Galerkin Finite
Element Methods for Parabolic Problems, Springer Lecture Notes in
Mathematics, No. 1054, from 1984. This has been out of print for
several years, and I have felt a need and been encouraged by
colleagues and friends to publish an updated version. In doing so I
have included most of the contents of the 14 chapters of the
earlier work in an updated and revised form, and added four new
chapters, on semigroup methods, on multistep schemes, on incomplete
iterative solution of the linear algebraic systems at the time
levels, and on semilineax equations. The old chapters on fully
discrete methods have been reworked by first treating the time
discretization of an abstract differential equation in a Hilbert
space setting, and the chapter on the discontinuous Galerkin method
has been completely rewritten.
目錄：
Preface
Preface to the Second Edition
1. The Standard Galerkin Method
2. Methods Based on More General Approximations
of the Elliptic Problem
3. Nonsmooth Data Error Estimates
4. More General Parabolic Equations
5. Negative Norm Estimates and Superconvergence
6. Maximum-Norm Estimates and Analytic Semigroups
7. Single Step Fully Discrete Schemes
for the Homogeneous Equation
8. Single Step Fully Discrete Schemes for the
Inhomogeneous Equation
9. Single Step Methods and Rational Approximations
of Semigroups
10. Multistep Backward Difference Methods
11. Incomplete Iterative Solution of the Algebraic Systems
at the Time Levels
12. The Discontinuous Galerkin Time Stepping Method
13. A Nonlinear Problem
14. Semilinear Parabolic Equations
15. The Method of Lumped Masses
16. The H1 and H-1 Methods
17. A Mixed Method
18. A Singular Problem
19. Problems in Polygonal Domains
20. Time Discretization by Laplace Transformation and Quadrature
References
Index
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