1.

Record Nr.

UNINA9910144940803321

Autore

Melenk Jens M. <1967->

Titolo

Hp-finite element methods for singular perturbations / / Jens M. Melenk

Pubbl/distr/stampa

Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2002

ISBN

3-540-45781-X

Descrizione fisica

1 online resource (xiv, 326 pages)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 1796

Classificazione

65N30

35B25

Disciplina

515.353

Soggetti

Differential equations, Partial - Numerical solutions

Singular perturbations (Mathematics)

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references (pages [311]-316) and index.

Nota di contenuto

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.

Sommario/riassunto

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.