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  • © 2002

hp-Finite Element Methods for Singular Perturbations

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1796)

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Table of contents (10 chapters)

  1. Front Matter

    Pages N2-XIV
  2. 1. Introduction

    • Jens M. Melenk
    Pages 1-20
  3. 3. hp Approximation

    • Jens M. Melenk
    Pages 73-138
  4. 4. The Countably Normed Spaces

    • Jens M. Melenk
    Pages 141-168
  5. 7. Regularity through Asymptotic Expansions

    • Jens M. Melenk
    Pages 255-295
  6. Appendix

    • Jens M. Melenk
    Pages 297-310
  7. References

    • Jens M. Melenk
    Pages 311-316
  8. Index

    • Jens M. Melenk
    Pages 317-318
  9. Back Matter

    Pages 319-323

About this book

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.

Keywords

  • FEM
  • design
  • elliptic regularity
  • finite element method
  • fluid mechanics
  • high order method
  • modeling
  • non-smooth domains
  • singular perturbation
  • spectral method
  • partial differential equations

Bibliographic Information

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions