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＜電子ブック＞
Galerkin Finite Element Methods for Parabolic Problems / by Vidar Thomee
(Springer Series in Computational Mathematics. ISSN:21983712 ; 25)

版	2nd ed. 2006.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2006
本文言語	英語
大きさ	XII, 364 p : online resource
著者標目	*Thomee, Vidar author SpringerLink (Online service)
件　名	LCSH:Numerical analysis LCSH:Mathematical analysis LCSH:Mathematical physics FREE:Numerical Analysis FREE:Analysis FREE:Theoretical, Mathematical and Computational Physics
一般注記	The Standard Galerkin Method -- Methods Based on More General Approximations of the Elliptic Problem -- Nonsmooth Data Error Estimates -- More General Parabolic Equations -- Negative Norm Estimates and Superconvergence -- Maximum-Norm Estimates and Analytic Semigroups -- Single Step Fully Discrete Schemes for the Homogeneous Equation -- Single Step Fully Discrete Schemes for the Inhomogeneous Equation -- Single Step Methods and Rational Approximations of Semigroups -- Multistep Backward Difference Methods -- Incomplete Iterative Solution of the Algebraic Systems at the Time Levels -- The Discontinuous Galerkin Time Stepping Method -- A Nonlinear Problem -- Semilinear Parabolic Equations -- The Method of Lumped Masses -- The H1 and H?1 Methods -- A Mixed Method -- A Singular Problem -- Problems in Polygonal Domains -- Time Discretization by Laplace Transformation and Quadrature This book provides insight in the mathematics of Galerkin finite element method as applied to parabolic equations. The approach is based on first discretizing in the spatial variables by Galerkin's method, using piecewise polynomial trial functions, and then applying some single step or multistep time stepping method. The concern is stability and error analysis of approximate solutions in various norms, and under various regularity assumptions on the exact solution. The book gives an excellent insight in the present ideas and methods of analysis. The second edition has been influenced by recent progress in application of semigroup theory to stability and error analysis, particulatly in maximum-norm. Two new chapters have also been added, dealing with problems in polygonal, particularly noncovex, spatial domains, and with time discretization based on using Laplace transformation and quadrature HTTP:URL=https://doi.org/10.1007/3-540-33122-0

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