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Record Nr. |
UNINA9910144940803321 |
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Autore |
Melenk Jens M. <1967-> |
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Titolo |
Hp-finite element methods for singular perturbations / / Jens M. Melenk |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2002 |
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ISBN |
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Descrizione fisica |
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1 online resource (xiv, 326 pages) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 1796 |
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Classificazione |
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Disciplina |
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Soggetti |
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Differential equations, Partial - Numerical solutions |
Singular perturbations (Mathematics) |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references (pages [311]-316) and index. |
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Nota di contenuto |
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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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Sommario/riassunto |
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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. |
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