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Discontinuous Galerkin Methods for Elliptic Problems

  • Douglas N. Arnold
  • Franco Brezzi
  • Bernardo Cockburn
  • Donatella Marini
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 11)

Abstract

We provide a common framework for the understanding, comparison, and analysis of several discontinuous Galerkin methods that have been proposed for the numerical treatment of elliptic problems. This class includes the recently introduced methods of Bassi and Rebay (together with the variants proposed by Brezzi, Manzini, Marini, Pietra and Russo), the local discontinuous Galerkin methods of Cockburn and Shu, and the method of Baumann and Oden. It also includes the so-called interior penalty methods developed some time ago by Douglas and Dupont, Wheeler, Baker, and Arnold among others.

Keywords

Elliptic Problem Discontinuous Galerkin Discontinuous Galerkin Method Finite Element Space Numerical Flux 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Douglas N. Arnold
    • 1
  • Franco Brezzi
    • 2
  • Bernardo Cockburn
    • 3
  • Donatella Marini
    • 2
  1. 1.Department of MathematicsPenn State UniversityUniversity ParkUSA
  2. 2.Dipartimento di Matematica and I.A.N.-C.N.R.PaviaItaly
  3. 3.School of MathematicsUniversity of MinnesotaMinneapolisUSA

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