03131nam 22005895 450 991014494080332120211202193453.03-540-45781-X10.1007/b84212(CKB)1000000000233286(SSID)ssj0000323844(PQKBManifestationID)11240565(PQKBTitleCode)TC0000323844(PQKBWorkID)10300897(PQKB)11607940(DE-He213)978-3-540-45781-7(MiAaPQ)EBC6285731(MiAaPQ)EBC5592388(Au-PeEL)EBL5592388(OCoLC)1066200133(PPN)155176439(EXLCZ)99100000000023328620121227d2002 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierHp-finite element methods for singular perturbations /Jens M. MelenkBerlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2002.1 online resource (xiv, 326 pages)Lecture Notes in Mathematics,0075-8434 ;17963-540-44201-4 Includes bibliographical references (pages [311]-316) and index.1.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.Many 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.Lecture notes in mathematics (Springer-Verlag) ;1796Differential equations, PartialNumerical solutionsSingular perturbations (Mathematics)Differential equations, PartialNumerical solutions.Singular perturbations (Mathematics)515.35365N30msc35B25mscMelenk Jens M.1967-67476MiAaPQMiAaPQMiAaPQBOOK9910144940803321Hp-finite element methods for singular perturbations262255UNINA