Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations, 1st Edition

  • Published By:
  • ISBN-10: 3319018183
  • ISBN-13: 9783319018188
  • DDC: 620.001515
  • Grade Level Range: College Freshman - College Senior
  • 279 Pages | eBook
  • Original Copyright 2014 | Published/Released June 2014
  • This publication's content originally published in print form: 2014

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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.

Table of Contents

Front Cover.
Other Frontmatter.
Title Page.
Copyright Page.
1: A Quick Tutorial on dg Methods for Elliptic Problems.
2: Discontinuous Galerkin Method for Time-Dependent Problems: Survey and Recent Developments.
3: Adaptivity and Error Estimation for Discontinuous Galerkin Methods.
4: A Quadratic C0 Interior Penalty Method for an Elliptic Optimal Control Problem with State Constraints.
5: A Local Timestepping Runge–kutta Discontinuous Galerkin Method for Hurricane Storm Surge Modeling.
6: An Overview of the Discontinuous Petrov Galerkin Method.
7: Discontinuous Galerkin for the Radiative Transport Equation.
8: Error Control for Discontinuous Galerkin Methods for First Order Hyperbolic Problems.
9: Virtual Element and Discontinuous Galerkin Methods.
10: A Dg Approach to Higher Order ale Formulations in Time.
11: Discontinuous Finite Element Methods for Coupled Surface–subsurface Flow and Transport Problems.