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AuthorMelenk, Jens M. author
Titlehp-Finite Element Methods for Singular Perturbations [electronic resource] / by Jens M. Melenk
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 2002
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Descript XIV, 326 p. online resource


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


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

Mathematics Mathematical analysis Analysis (Mathematics) Global analysis (Mathematics) Manifolds (Mathematics) Partial differential equations Numerical analysis Applied mathematics Engineering mathematics Mechanical engineering Mathematics Analysis Appl.Mathematics/Computational Methods of Engineering Mechanical Engineering Numerical Analysis Global Analysis and Analysis on Manifolds Partial Differential Equations


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