Advertisement

hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes

  • Andrea Cangiani
  • Zhaonan Dong
  • Emmanuil H. Georgoulis
  • Paul Houston
Book
  • 4.1k Downloads

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis, Paul Houston
    Pages 1-9
  3. Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis, Paul Houston
    Pages 11-22
  4. Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis, Paul Houston
    Pages 23-37
  5. Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis, Paul Houston
    Pages 39-55
  6. Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis, Paul Houston
    Pages 57-85
  7. Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis, Paul Houston
    Pages 87-103
  8. Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis, Paul Houston
    Pages 105-120
  9. Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis, Paul Houston
    Pages 121-122
  10. Back Matter
    Pages 123-131

About this book

Introduction

Over the last few decades discontinuous Galerkin finite element methods (DGFEMs) have been witnessed tremendous interest as a computational framework for the numerical solution of partial differential equations. Their success is due to their extreme versatility in the design of the underlying meshes and local basis functions, while retaining key features of both (classical) finite element and finite volume methods. Somewhat surprisingly, DGFEMs on general tessellations consisting of polygonal (in 2D) or polyhedral (in 3D) element shapes have received little attention within the literature, despite the potential computational advantages.

This volume introduces the basic principles of hp-version (i.e., locally varying mesh-size and polynomial order) DGFEMs over meshes consisting of polygonal or polyhedral element shapes, presents their error analysis, and includes an extensive collection of numerical experiments. The extreme flexibility provided by the locally variable elemen

t-shapes, element-sizes, and element-orders is shown to deliver substantial computational gains in several practical scenarios.  

Keywords

Discontinuous Galerkin method Finite element method Hp-version Polygonal and polyhedral meshes partial differential equations

Authors and affiliations

  • Andrea Cangiani
    • 1
  • Zhaonan Dong
    • 2
  • Emmanuil H. Georgoulis
    • 3
  • Paul Houston
    • 4
  1. 1.Department of MathematicsUniversity of LeicesterLeicesterUnited Kingdom
  2. 2.Department of MathematicsUniversity of LeicesterLeicesterUnited Kingdom
  3. 3.Department of MathematicsUniversity of LeicesterLeicesterUnited Kingdom
  4. 4.School of Mathematical SciencesUniversity of NottinghamNottinghamUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-67673-9
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-67671-5
  • Online ISBN 978-3-319-67673-9
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site