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.
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
