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抛物型问题的伽略金有限元方法(英文版)

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抛物型问题的伽略金有限元方法(英文版)

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作 者:V.Thomee 著

出 版 社:世界图书出版公司

出版时间:2003-6-1

I S B N:9787506259576

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内容简介

My purpose in this monograph is to present an essentially self-contained account of the mathematical theory of Galerkin finite element methods as applied to parabolic partial differential equations. The emphases and selection of topics reflects my own involvement in the field over the past 25 years, and my ambition has been to stress ideas and methods of analysis rather than to describe the most general and farreaching results possible. Since the formulation and analysis of Galerkin finite element methods for parabolic problems are generally based on ideas and results from the corresponding theory for stationary elliptic problems, such material is often included in the presentation.

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目录

Preface
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. Maximum-Norm Stability and Error Estimates
6. Negative Norm Estimates and Superconvergence
7. Single Step Fully Discrete Schemes for the Homogeneous Equation
8. Single Step Methods and Rational Approximations of Semigroups
9. Single Step Fully Discrete Schemes for the Inhomogeneous Equation
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
References
Index

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