Author	Melenk, Jens M. author
Title	hp-Finite Element Methods for Singular Perturbations [electronic resource] / by Jens M. Melenk
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 2002
Connect to	http://dx.doi.org/10.1007/b84212
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

1. Mathematics
2. Mathematical analysis
3. Analysis (Mathematics)
4. Global analysis (Mathematics)
5. Manifolds (Mathematics)
6. Partial differential equations
7. Numerical analysis
8. Applied mathematics
9. Engineering mathematics
10. Mechanical engineering
11. Mathematics
12. Analysis
13. Appl.Mathematics/Computational Methods of Engineering
14. Mechanical Engineering
15. Numerical Analysis
16. Global Analysis and Analysis on Manifolds
17. Partial Differential Equations