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Lecture Notes in Mathematics

hp-Finite Element Methods for Singular Perturbations

Authors: Melenk, Jens M.

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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.

Table of contents (10 chapters)

  • 1. Introduction

    Melenk, Jens M.

    Pages 1-20

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

    Melenk, Jens M.

    Pages 23-72

  • 3. hp Approximation

    Melenk, Jens M.

    Pages 73-138

  • 4. The Countably Normed Spaces

    Melenk, Jens M.

    Pages 141-168

  • 5. Regularity Theory in Countably Normed Spaces

    Melenk, Jens M.

    Pages 169-224

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-540-45781-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.95
price for USA
  • ISBN 978-3-540-44201-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
hp-Finite Element Methods for Singular Perturbations
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1796
Copyright
2002
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-45781-7
DOI
10.1007/b84212
Softcover ISBN
978-3-540-44201-1
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIV, 326
Topics