hp-Finite Element Methods for Singular Perturbations

  • Authors
  • Jens┬áM.┬áMelenk

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

Table of contents

  1. Front Matter
    Pages N2-XIV
  2. Jens M. Melenk
    Pages 1-20
  3. Jens M. Melenk
    Pages 73-138
  4. Jens M. Melenk
    Pages 255-295
  5. Jens M. Melenk
    Pages 297-310
  6. Jens M. Melenk
    Pages 311-316
  7. Jens M. Melenk
    Pages 317-318
  8. Back Matter
    Pages 319-323

About this book

Introduction

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

Bibliographic information

  • DOI https://doi.org/10.1007/b84212
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-44201-1
  • Online ISBN 978-3-540-45781-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book