抛物问题的伽辽金有限元方法 : 第2版

PrefacePreface to the Second Edition1. The Standard Galerkin Method2. Methods Based on More General Approximations of the Elliptic Problem3. Nonsmooth Data Error Estimates4. More General Parabolic Equations5. Negative Norm Estimates and Superconvergence6. Maximum-Norm Estimates and Analytic Semigroups7. Single Step Fully Discrete Schemes for the Homogeneous Equation8. Single Step Fully Discrete Schemes for the Inhomogeneous Equation9. Single Step Methods and Rational Approximations of Semigroups10. Multistep Backward Difference Methods11. Incomplete Iterative Solution of the Algebraic Systems at the Time Levels12. The Discontinuous Galerkin Time Stepping Method13. A Nonlinear Problem14. Semilinear Parabolic Equations15. The Method of Lumped Masses16. The H1 and H-1 Methods17. A Mixed Method18. A Singular Problem19. Problems in Polygonal Domains20. Time Discretization by Laplace Transformation and QuadratureReferencesIndex

《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：Thebasis of this work is my earlier text entitled Galerkin FiniteElement Methods for Parabolic Problems, Springer Lecture Notes inMathematics, No. 1054, from 1984. This has been out of print forseveral years, and I have felt a need and been encouraged bycolleagues and friends to publish an updated version. In doing so Ihave included most of the contents of the 14 chapters of theearlier work in an updated and revised form, and added four newchapters, on semigroup methods, on multistep schemes, on incompleteiterative solution of the linear algebraic systems at the timelevels, and on semilineax equations. The old chapters on fullydiscrete methods have been reworked by first treating the timediscretization of an abstract differential equation in a Hilbertspace setting, and the chapter on the discontinuous Galerkin methodhas been completely rewritten.