HP-finite element methods for singular perturbations
Author(s)
Bibliographic Information
HP-finite element methods for singular perturbations
(Lecture notes in mathematics, 1796)
Springer, c2002
Available at / 67 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||179678800542
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INTERNATIONAL CHRISTIAN UNIVERSITY LIBRARY図
V.1796410.8/L507/v.179605856941,
410.8/L507/v.179605856941 -
Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC21:515.353/M8432070575542
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Note
Bibliography: p. [311]-316
Includes index
Description and Table of Contents
Description
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.
Table of Contents
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.
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