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

1. Front Matter

   Pages i-xii

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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

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.

• A Priori and a Posteriori Error Estimates
• Adaptivity
• Discontinuous Galerkin Methods
• Partial Differential Equations

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

  Xiaobing Feng, Ohannes Karakashian, Yulong Xing

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