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SpringerBriefs in Mathematics

hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes

Authors: Cangiani, A., Dong, Z., Georgoulis, E.H., Houston, P.

  • Self-contained introduction to discontinuous Galerkin methods
  • Extensive discussion on computer implementation of the methods presented 
  • Cutting edge extensions of the very popular discontinuous Galerkin methods, explained in detail
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eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-67673-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-3-319-67671-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.  

Table of contents (8 chapters)

  • Introduction

    Cangiani, Andrea (et al.)

    Pages 1-9

  • Introduction to Discontinuous Galerkin Methods

    Cangiani, Andrea (et al.)

    Pages 11-22

  • Inverse Estimates and Polynomial Approximation on Polytopic Meshes

    Cangiani, Andrea (et al.)

    Pages 23-37

  • DGFEMs for Pure Diffusion Problems

    Cangiani, Andrea (et al.)

    Pages 39-55

  • DGFEMs for Second-Order PDEs of Mixed-Type

    Cangiani, Andrea (et al.)

    Pages 57-85

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-67673-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-3-319-67671-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-67673-9
DOI
10.1007/978-3-319-67673-9
Softcover ISBN
978-3-319-67671-5
Series ISSN
2191-8198
Edition Number
1
Number of Pages
VIII, 131
Number of Illustrations and Tables
31 b/w illustrations, 1 illustrations in colour
Topics