《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.

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