000 03769nam a22005055i 4500
001 978-3-540-33122-3
003 DE-He213
005 20181204131310.0
007 cr nn 008mamaa
008 100301s2006 gw | s |||| 0|eng d
020 _a9783540331223
_9978-3-540-33122-3
024 7 _a10.1007/3-540-33122-0
_2doi
040 _aISI Library, Kolkata
050 4 _aQA297-299.4
072 7 _aPBKS
_2bicssc
072 7 _aMAT021000
_2bisacsh
072 7 _aPBKS
_2thema
082 0 4 _a518
_223
100 1 _aThomée, Vidar.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aGalerkin Finite Element Methods for Parabolic Problems
_h[electronic resource] /
_cby Vidar Thomée.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2006.
300 _aXII, 364 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Series in Computational Mathematics,
_x0179-3632 ;
_v25
505 0 _aThe 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.
520 _aThis 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.
650 0 _aNumerical analysis.
650 0 _aGlobal analysis (Mathematics).
650 1 4 _aNumerical Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M14050
650 2 4 _aAnalysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12007
650 2 4 _aTheoretical, Mathematical and Computational Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19005
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540822028
776 0 8 _iPrinted edition:
_z9783642069673
776 0 8 _iPrinted edition:
_z9783540331216
830 0 _aSpringer Series in Computational Mathematics,
_x0179-3632 ;
_v25
856 4 0 _uhttps://doi.org/10.1007/3-540-33122-0
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c425201
_d425201