作者：托姆
页数：370
出版社：世界图书出版公司
出版日期：2013
ISBN：9787510058370
电子书格式：pdf/epub/txt
内容简介
本书深刻的讲述了Galerkin有限元方法及其在抛物方程中的应用。这是第二版，受最新理论成果-半群在稳定性和误差分析中应用，尤其是最大模的影响，在原来的基础上做了大量的修订。新增加了两章讲述多项式、非凸性、空间域以及基于拉普拉斯变换的时间离散化和求面积。标准Galerkin方法；基于更多椭圆问题一般逼近的方法；非光滑数据误差估计；更多一般抛物方程；负标准估计和超收敛；最大标准估计和解析半群；齐次方程的单步完全离散型；非其次方程的单步完全离散型；多步向后差分方法；时间层次的代数系统不完全迭代解；非连续Galerkin时间自适应方法；非线性问题；半线性抛物方程；集中质量方法；H1和H1方法；混合方法；奇异问题；多边域问题；基于拉普拉斯变换的时间离散化和求面积。
作者简介
Vidar Thomée是国际知名学者，在数学和物理学界享有盛誉。本书凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。
本书特色
《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.
目录
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
节选
《抛物问题的伽辽金有限元方法(第2版)(英文)》适用于数学专业的研究生、以及更高层次的科研人员和数学工作者。
