Jens M. Melenk

hp-Finite Element Methods for Singular Perturbations (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 326
• Erscheinungstermin: 19. Oktober 2004
• Englisch
• ISBN-13: 9783540457817
• Artikelnr.: 53086296

Autorenporträt

Jens M. Melenk, Max-Planck-Institute for Mathematics in the Sciences, Leipzig, Germany

Inhaltsangabe

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.