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Anisotropic hp-Mesh Adaptation Methods

Theory, implementation and applications

  • Book
  • © 2022

Overview

Authors:
  1. Vít Dolejší

    1. Faculty of Mathematics & Physics, Charles University, Praha 8, Czech Republic

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  2. Georg May

    1. Aeronautics and Aerospace, Von Karman Institute for Fluid Dynamics, Sint-Genesius-Rode, Belgium

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • First monograph exploring the anisotropic hp-mesh adaptation method
  • Presents rigorous theoretical results that are directly exploitable in practical computations
  • Demonstrates techniques through many numerical experimants

Part of the book series: Nečas Center Series (NECES)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    • Vít Dolejší, Georg May
    Pages 1-18

  3. Metric Based Mesh Representation

    • Vít Dolejší, Georg May
    Pages 19-41

  4. Interpolation Error Estimates for Two Dimensions

    • Vít Dolejší, Georg May
    Pages 43-76

  5. Interpolation Error Estimates for Three Dimensions

    • Vít Dolejší, Georg May
    Pages 77-88

  6. Anisotropic Mesh Adaptation Method, h-Variant

    • Vít Dolejší, Georg May
    Pages 89-132

  7. Anisotropic Mesh Adaptation Method, hp-Variant

    • Vít Dolejší, Georg May
    Pages 133-154

  8. Framework of the Goal-Oriented Error Estimates

    • Vít Dolejší, Georg May
    Pages 155-184

  9. Goal-Oriented Anisotropic Mesh Adaptation

    • Vít Dolejší, Georg May
    Pages 185-215

  10. Implementation Aspects

    • Vít Dolejší, Georg May
    Pages 217-227

  11. Applications

    • Vít Dolejší, Georg May
    Pages 229-241

  12. Back Matter

    Pages 243-252
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Keywords

About this book

Mesh adaptation methods can have a profound impact on the numerical solution of partial differential equations.  If devised and implemented properly, adaptation significantly reduces the size of the algebraic systems resulting from the discretization, while ensuring that applicable error tolerances are met. In this monograph, drawing from many years of experience, the authors give a comprehensive presentation of metric-based anisotropic hp-mesh adaptation methods.


A large part of this monograph is devoted to the derivation of computable interpolation error estimates on simplicial meshes, which take into account the geometry of mesh elements as well as the anisotropic features of the interpolated function. These estimates are then used for the optimization of corresponding finite element spaces in a variety of settings. Both steady and time dependent problems are treated, as well as goal-oriented adaptation. Practical aspects of implementation are also explored, including several algorithms. Many numerical experiments using the discontinuous Galerkin method are presented to illustrate the performance of the adaptive techniques.


This monograph is intended for scientists and researchers, including doctoral and master-level students. Portions of the text can also be used as study material for advanced university lectures concerning a posteriori error analysis and mesh adaptation.

Authors and Affiliations

  • Faculty of Mathematics & Physics, Charles University, Praha 8, Czech Republic

    Vít Dolejší

  • Aeronautics and Aerospace, Von Karman Institute for Fluid Dynamics, Sint-Genesius-Rode, Belgium

    Georg May

Bibliographic Information

  • Book Title: Anisotropic hp-Mesh Adaptation Methods

  • Book Subtitle: Theory, implementation and applications

  • Authors: Vít Dolejší, Georg May

  • Series Title: Nečas Center Series

  • DOI: https://doi.org/10.1007/978-3-031-04279-9

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

  • Softcover ISBN: 978-3-031-04278-2Published: 07 June 2022

  • eBook ISBN: 978-3-031-04279-9Published: 06 June 2022

  • Series ISSN: 2523-3343

  • Series E-ISSN: 2523-3351

  • Edition Number: 1

  • Number of Pages: X, 252

  • Number of Illustrations: 18 b/w illustrations, 87 illustrations in colour

  • Topics: Numerical Analysis, Computational Science and Engineering

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