000 03605nam a22005775i 4500
001 978-3-540-45781-7
003 DE-He213
005 20190213151203.0
007 cr nn 008mamaa
008 121227s2002 gw | s |||| 0|eng d
020 _a9783540457817
_9978-3-540-45781-7
024 7 _a10.1007/b84212
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBK
_2thema
082 0 4 _a515
_223
100 1 _aMelenk, Jens M.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _ahp-Finite Element Methods for Singular Perturbations
_h[electronic resource] /
_cby Jens M. Melenk.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2002.
300 _aXIV, 326 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1796
505 0 _a1.Introduction -- Part I: Finite Element Approximation -- 2. hp-FEM for Reaction Diffusion Problems: Principal Results -- 3. hp Approximation -- Part II: Regularity in Countably Normed Spaces -- 4. The Countably Normed Spaces blb,e -- 5. Regularity Theory in Countably Normed Spaces -- Part III: Regularity in Terms of Asymptotic Expansions -- 6. Exponentially Weighted Countably Normed Spaces -- Appendix -- References -- Index.
520 _aMany partial differential equations arising in practice are parameter-dependent problems that are of singularly perturbed type. Prominent examples include plate and shell models for small thickness in solid mechanics, convection-diffusion problems in fluid mechanics, and equations arising in semi-conductor device modelling. Common features of these problems are layers and, in the case of non-smooth geometries, corner singularities. Mesh design principles for the efficient approximation of both features by the hp-version of the finite element method (hp-FEM) are proposed in this volume. For a class of singularly perturbed problems on polygonal domains, robust exponential convergence of the hp-FEM based on these mesh design principles is established rigorously.
650 0 _aGlobal analysis (Mathematics).
650 0 _aEngineering mathematics.
650 0 _aMechanical engineering.
650 0 _aNumerical analysis.
650 0 _aGlobal analysis.
650 0 _aDifferential equations, partial.
650 1 4 _aAnalysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12007
650 2 4 _aMathematical and Computational Engineering.
_0http://scigraph.springernature.com/things/product-market-codes/T11006
650 2 4 _aMechanical Engineering.
_0http://scigraph.springernature.com/things/product-market-codes/T17004
650 2 4 _aNumerical Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M14050
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
_0http://scigraph.springernature.com/things/product-market-codes/M12082
650 2 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662175804
776 0 8 _iPrinted edition:
_z9783540442011
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1796
856 4 0 _uhttps://doi.org/10.1007/b84212
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c9818
_d9818