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Discontinuous Galerkin Methods

Theory, Computation and Applications

  • Conference proceedings
  • © 2000

Overview

Editors:
  1. Bernardo Cockburn

    1. School of Mathematics, University of Minnesota, Minneapolis, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. George E. Karniadakis

    1. Division of Applied Mathematics, Brown University, Providence, USA

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    You can also search for this editor in PubMed   Google Scholar

  3. Chi-Wang Shu

    1. Division of Applied Mathematics, Brown University, Providence, USA

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Part of the book series: Lecture Notes in Computational Science and Engineering (LNCSE, volume 11)

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Table of contents (49 papers)

  1. Front Matter

    Pages I-XI
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  2. Overview

    1. Front Matter

      Pages 1-1
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    2. The Development of Discontinuous Galerkin Methods

      • Bernardo Cockburn, George E. Karniadakis, Chi-Wang Shu
      Pages 3-50

  3. Invited Papers

    1. Front Matter

      Pages 51-51
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    2. Steps Toward a Robust High-Order Simulation Tool for Aerospace Applications

      • Harold L. Atkins
      Pages 53-61

    3. Simplified Discontinuous Galerkin Methods for Systems of Conservation Laws with Convex Extension

      • Timothy J. Barth
      Pages 63-75

    4. A High Order Discontinuous Galerkin Method for Compressible Turbulent Flows

      • F. Bassi, S. Rebay
      Pages 77-88

    5. Discontinuous Galerkin Methods for Elliptic Problems

      • Douglas N. Arnold, Franco Brezzi, Bernardo Cockburn, Donatella Marini
      Pages 89-101

    6. Analysis of Finite Element Methods for Linear Hyperbolic Problems

      • Richard S. Falk
      Pages 103-112

    7. Software for the Parallel Adaptive Solution of Conservation Laws by Discontinuous Galerkin Methods

      • J. E. Flaherty, R. M. Loy, M. S. Shephard, J. D. Teresco
      Pages 113-123

    8. Simulation of Gravity Flow of Granular Materials in Silos

      • Pierre A. Gremaud, John V. Matthews
      Pages 125-134

    9. A Comparison of Discontinuous and Continuous Galerkin Methods Based on Error Estimates, Conservation, Robustness and Efficiency

      • Thomas J. R. Hughes, Gerald Engel, Luca Mazzei, Mats G. Larson
      Pages 135-146

    10. The Utility of Modeling and Simulation in Determining Transport Performance Properties of Semiconductors

      • Bernardo Cockburn, Joseph W. Jerome, Chi-Wang Shu
      Pages 147-156

    11. A Discontinuous Galerkin Method for the Incompressible Navier-Stokes Equations

      • Ohannes Karakashian, Theodoros Katsaounis
      Pages 157-166

    12. Full Convergence for Hyperbolic Finite Elements

      • Qun Lin
      Pages 167-177

    13. A Conservative DGM for Convection-Diffusion and Navier-Stokes Problems

      • J. Tinsley Oden, Carlos Erik Baumann
      Pages 179-196

    14. GMRES Discontinuous Galerkin Solution of the Compressible Navier-Stokes Equations

      • F. Bassi, S. Rebay
      Pages 197-208

    15. Explicit Finite Element Methods for Linear Hyperbolic Systems

      • Richard S. Falk, Gerard R. Richter
      Pages 209-219

    16. hp-DGFEM for Partial Differential Equations with Nonnegative Characteristic Form

      • Endre Süli, Christoph Schwab, Paul Houston
      Pages 221-230

    17. A Discontinuous Galerkin Method Applied to Nonlinear Parabolic Equations

      • Béatrice Rivière, Mary F. Wheeler
      Pages 231-244
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Keywords

About this book

A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula­ tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead­ ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz­ ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.

Editors and Affiliations

  • School of Mathematics, University of Minnesota, Minneapolis, USA

    Bernardo Cockburn

  • Division of Applied Mathematics, Brown University, Providence, USA

    George E. Karniadakis, Chi-Wang Shu

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