LEADER 03131nam 22005895 450 001 9910144940803321 005 20211202193453.0 010 $a3-540-45781-X 024 7 $a10.1007/b84212 035 $a(CKB)1000000000233286 035 $a(SSID)ssj0000323844 035 $a(PQKBManifestationID)11240565 035 $a(PQKBTitleCode)TC0000323844 035 $a(PQKBWorkID)10300897 035 $a(PQKB)11607940 035 $a(DE-He213)978-3-540-45781-7 035 $a(MiAaPQ)EBC6285731 035 $a(MiAaPQ)EBC5592388 035 $a(Au-PeEL)EBL5592388 035 $a(OCoLC)1066200133 035 $a(PPN)155176439 035 $a(EXLCZ)991000000000233286 100 $a20121227d2002 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHp-finite element methods for singular perturbations /$fJens M. Melenk 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2002. 215 $a1 online resource (xiv, 326 pages) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1796 311 $a3-540-44201-4 320 $aIncludes bibliographical references (pages [311]-316) and index. 327 $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. 330 $aMany partial differential equations arising in practice are parameter-dependent problems that are of singularly perturbed type. Prominent examples include plate and shell models for small thickness in solid mechanics, convection-diffusion problems in fluid mechanics, and equations arising in semi-conductor device modelling. Common features of these problems are layers and, in the case of non-smooth geometries, corner singularities. Mesh design principles for the efficient approximation of both features by the hp-version of the finite element method (hp-FEM) are proposed in this volume. For a class of singularly perturbed problems on polygonal domains, robust exponential convergence of the hp-FEM based on these mesh design principles is established rigorously. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1796 606 $aDifferential equations, Partial$xNumerical solutions 606 $aSingular perturbations (Mathematics) 615 0$aDifferential equations, Partial$xNumerical solutions. 615 0$aSingular perturbations (Mathematics) 676 $a515.353 686 $a65N30$2msc 686 $a35B25$2msc 700 $aMelenk$b Jens M.$f1967-$067476 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910144940803321 996 $aHp-finite element methods for singular perturbations$9262255 997 $aUNINA