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An Invitation to the Theory of the Hybridizable Discontinuous Galerkin Method

Projections, Estimates, Tools

  • Shukai  Du
  • Francisco-Javier Sayas
Book

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-x
  2. Shukai Du, Francisco-Javier Sayas
    Pages 1-5
  3. Shukai Du, Francisco-Javier Sayas
    Pages 7-44
  4. Shukai Du, Francisco-Javier Sayas
    Pages 45-67
  5. Shukai Du, Francisco-Javier Sayas
    Pages 69-84
  6. Shukai Du, Francisco-Javier Sayas
    Pages 85-112
  7. Shukai Du, Francisco-Javier Sayas
    Pages 113-114
  8. Back Matter
    Pages 115-124

About this book

Introduction

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.

Keywords

Discontinuous Galerkin Method Partial Differential Equations Hybridization Mixed finite element methods Galerkin Method Projection-based error analysis

Authors and affiliations

  • Shukai  Du
    • 1
  • Francisco-Javier Sayas
    • 2
  1. 1.Mathematical SciencesUniversity of DelawareNewarkUSA
  2. 2.Mathematical SciencesUniversity of DelawareNewarkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-27230-2
  • Copyright Information The Author(s), under exclusive license to Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-27229-6
  • Online ISBN 978-3-030-27230-2
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site