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hp-Finite Element Methods for Singular Perturbations

  • Book
  • © 2002

Overview

Authors:
  1. Jens M. Melenk
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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
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  2. 1. Introduction

    • Jens M. Melenk
    Pages 1-20

  3. 2. hp-FEM for Reaction Diffusion Problems: Principal Results

    • Jens M. Melenk
    Pages 23-72

  4. 3. hp Approximation

    • Jens M. Melenk
    Pages 73-138

  5. 4. The Countably Normed Spaces

    • Jens M. Melenk
    Pages 141-168

  6. 5. Regularity Theory in Countably Normed Spaces

    • Jens M. Melenk
    Pages 169-224

  7. 6. Exponentially Weighted Countably Normed Spaces

    • Jens M. Melenk
    Pages 227-254

  8. 7. Regularity through Asymptotic Expansions

    • Jens M. Melenk
    Pages 255-295

  9. Appendix

    • Jens M. Melenk
    Pages 297-310

  10. References

    • Jens M. Melenk
    Pages 311-316

  11. Index

    • Jens M. Melenk
    Pages 317-318

  12. Back Matter

    Pages 319-323
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Keywords

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.

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