hp-Finite Element Methods for Singular Perturbations

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.

List of contents

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.

Product details

• Authors: J. M. Melenk, Jens M. Melenk
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 10.10.2002
• EAN: 9783540442011
• ISBN: 978-3-540-44201-1
• No. of pages: 326
• Dimensions: 156 mm x 237 mm x 20 mm
• Weight: 508 g
• Illustrations: XIV, 326 p.
• Series: Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; Maschinenbau, Analysis, B, Differentialrechnung und -gleichungen, Numerische Mathematik, Mathematics and Statistics, Mathematical and Computational Engineering, Mechanical Engineering, Numerical analysis, Manifolds (Mathematics), Partial Differential Equations, Differential calculus & equations, Differential equations, Engineering mathematics, Applied mathematics, Mathematical and Computational Engineering Applications, Maths for engineers, Analysis (Mathematics), Mathematical analysis, Global analysis (Mathematics), Global Analysis and Analysis on Manifolds