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An Invitation to the Theory of the Hybridizable Discontinuous Galerkin Method

Projections, Estimates, Tools

  • Book
  • © 2019

Overview

Authors:
  1. Shukai Du

    1. Mathematical Sciences, University of Delaware, Newark, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Francisco-Javier Sayas

    1. Mathematical Sciences, University of Delaware, Newark, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • First introduction to a systematic analysis of the Hybridizable Discontinuous Galerkin Method
  • Presentation of new simplified techniques to prove estimates using the well-established projection-based analysis of HDG methods
  • Covers applications to diffusion process (steady-state and evolutionary) and wave propagation (time-harmonic and transient)

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-x
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  2. Getting Ready

    • Shukai Du, Francisco-Javier Sayas
    Pages 1-5

  3. Projection Analysis of Mixed Methods

    • Shukai Du, Francisco-Javier Sayas
    Pages 7-44

  4. The Hybridizable Discontinuous Galerkin Method

    • Shukai Du, Francisco-Javier Sayas
    Pages 45-67

  5. Variants of the HDG Method

    • Shukai Du, Francisco-Javier Sayas
    Pages 69-84

  6. HDG Methods for Evolutionary Equations

    • Shukai Du, Francisco-Javier Sayas
    Pages 85-112

  7. Further Reading

    • Shukai Du, Francisco-Javier Sayas
    Pages 113-114

  8. Back Matter

    Pages 115-124
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Keywords

About this book

This monograph requires basic knowledge of the variational theory of elliptic PDE and the techniques used for the analysis of the Finite Element Method. However, all the tools for the analysis of FEM (scaling arguments, finite dimensional estimates in the reference configuration, Piola transforms) are carefully introduced before being used, so that the reader does not need to go over longforgotten textbooks. Readers include: computational mathematicians, numerical analysts, engineers and scientists interested in new and computationally competitive Discontinuous Galerkin methods. The intended audience includes graduate students in computational mathematics, physics, and engineering, since the prerequisites are quite basic for a second year graduate student who has already taken a non necessarily advanced class in the Finite Element method.



Authors and Affiliations

  • Mathematical Sciences, University of Delaware, Newark, USA

    Shukai Du, Francisco-Javier Sayas

Bibliographic Information

  • Book Title: An Invitation to the Theory of the Hybridizable Discontinuous Galerkin Method

  • Book Subtitle: Projections, Estimates, Tools

  • Authors: Shukai Du, Francisco-Javier Sayas

  • Series Title: SpringerBriefs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-27230-2

  • Publisher: Springer Cham

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

  • Copyright Information: The Author(s), under exclusive license to Springer Nature Switzerland AG 2019

  • Softcover ISBN: 978-3-030-27229-6Published: 14 September 2019

  • eBook ISBN: 978-3-030-27230-2Published: 29 August 2019

  • Series ISSN: 2191-8198

  • Series E-ISSN: 2191-8201

  • Edition Number: 1

  • Number of Pages: X, 124

  • Number of Illustrations: 24 b/w illustrations

  • Topics: Numerical Analysis

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