|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNISA996466619003316 |
|
|
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 |
|
|
|
|
|
|
Descrizione fisica |
|
1 online resource (xiv, 326 pages) |
|
|
|
|
|
|
Collana |
|
Lecture Notes in Mathematics, , 0075-8434 ; ; 1796 |
|
|
|
|
|
|
Classificazione |
|
|
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
Differential equations, Partial - Numerical solutions |
Singular perturbations (Mathematics) |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
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. |
|
|
|
|
|
|
|