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Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations

2012 John H Barrett Memorial Lectures

  • Book
  • © 2014

Overview

Editors:
  1. Xiaobing Feng

    1. Department of Mathematics, The University of Tennessee, Knoxville, USA

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  2. Ohannes Karakashian

    1. Department of Mathematics, The University of Tennessee, Knoxville, USA

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    You can also search for this editor in PubMed   Google Scholar

  3. Yulong Xing

    1. Department of Mathematics, The University of Tennessee, Knoxville, USA

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  • Distinguished list of authors who are leading researchers on discontinuous Galerkin finite element methods
  • Several papers in the volume are survey papers on different aspects of discontinuous Galerkin finite element methods
  • The volume covers a broad aspects of discontinuous Galerkin finite element methods including method development and design, practical implementation, and emerging applications of discontinuous Galerkin finite element methods
  • Includes supplementary material: sn.pub/extras

Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 157)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. A Quick Tutorial on DG Methods for Elliptic Problems

    • F. Brezzi, L. D. Marini
    Pages 1-24

  3. Discontinuous Galerkin Method for Time-Dependent Problems: Survey and Recent Developments

    • Chi-Wang Shu
    Pages 25-62

  4. Adaptivity and Error Estimation for Discontinuous Galerkin Methods

    • Slimane Adjerid, Mahboub Baccouch
    Pages 63-96

  5. A Quadratic C 0 Interior Penalty Method for an Elliptic Optimal Control Problem with State Constraints

    • S. C. Brenner, L.-Y. Sung, Y. Zhang
    Pages 97-132

  6. A Local Timestepping Runge–Kutta Discontinuous Galerkin Method for Hurricane Storm Surge Modeling

    • Clint Dawson
    Pages 133-148

  7. An Overview of the Discontinuous Petrov Galerkin Method

    • Leszek F. Demkowicz, Jay Gopalakrishnan
    Pages 149-180

  8. Discontinuous Galerkin for the Radiative Transport Equation

    • Jean-Luc Guermond, Guido Kanschat, Jean C. Ragusa
    Pages 181-193

  9. Error Control for Discontinuous Galerkin Methods for First Order Hyperbolic Problems

    • Emmanuil H. Georgoulis, Edward Hall, Charalambos Makridakis
    Pages 195-207

  10. Virtual Element and Discontinuous Galerkin Methods

    • F. Brezzi, L. D. Marini
    Pages 209-221

  11. A dG Approach to Higher Order ALE Formulations in Time

    • Andrea Bonito, Irene Kyza, Ricardo H. Nochetto
    Pages 223-258

  12. Discontinuous Finite Element Methods for Coupled Surface–Subsurface Flow and Transport Problems

    • Beatrice Riviere
    Pages 259-279
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Keywords

About this book

The field of discontinuous Galerkin finite element methods has attracted considerable recent attention from scholars in the applied sciences and engineering. This volume brings together scholars working in this area, each representing a particular theme or direction of current research. Derived from the 2012 Barrett Lectures at the University of Tennessee, the papers reflect the state of the field today and point toward possibilities for future inquiry. The longer survey lectures, delivered by Franco Brezzi and Chi-Wang Shu, respectively, focus on theoretical aspects of discontinuous Galerkin methods for elliptic and evolution problems. Other papers apply DG methods to cases involving radiative transport equations, error estimates, and time-discrete higher order ALE functions, among other areas. Combining focused case studies with longer sections of expository discussion, this book will be an indispensable reference for researchers and students working with discontinuous Galerkin finite element methods and its applications.

Editors and Affiliations

  • Department of Mathematics, The University of Tennessee, Knoxville, USA

    Xiaobing Feng, Ohannes Karakashian, Yulong Xing

Bibliographic Information

  • Book Title: Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations

  • Book Subtitle: 2012 John H Barrett Memorial Lectures

  • Editors: Xiaobing Feng, Ohannes Karakashian, Yulong Xing

  • Series Title: The IMA Volumes in Mathematics and its Applications

  • DOI: https://doi.org/10.1007/978-3-319-01818-8

  • Publisher: Springer Cham

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

  • Copyright Information: Springer International Publishing Switzerland 2014

  • Hardcover ISBN: 978-3-319-01817-1Published: 21 November 2013

  • Softcover ISBN: 978-3-319-37840-4Published: 23 August 2016

  • eBook ISBN: 978-3-319-01818-8Published: 08 November 2013

  • Series ISSN: 0940-6573

  • Series E-ISSN: 2198-3224

  • Edition Number: 1

  • Number of Pages: XII, 279

  • Number of Illustrations: 14 b/w illustrations, 58 illustrations in colour

  • Topics: Numerical Analysis, Partial Differential Equations, Analysis

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