On the design of discontinuous Galerkin methods for elliptic problems based on hybrid formulations

Ramon Codina, Santiago Badia

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8 Citations (Scopus)

Abstract

The objective of this paper is to present a new framework for the design of discontinuous Galerkin (dG) methods for elliptic problems. The idea is to start from a hybrid formulation of the problem involving as unknowns the main field in the interior of the element domains and its fluxes and traces on the element boundaries. Rather than working with this three-field formulation, fluxes are modeled using finite difference expressions and then the traces are determined by imposing continuity of fluxes, although other strategies could be devised. This procedure is applied to four elliptic problems, namely, the convection-diffusion equation (in the diffusion dominated regime), the Stokes problem, the Darcy problem and the Maxwell problem. We justify some well known dG methods with some modifications that in fact allow to improve the performance of the original methods, particularly when the physical properties are discontinuous.

Original languageEnglish
Pages (from-to)158-168
Number of pages11
JournalComputer Methods in Applied Mechanics and Engineering
Volume263
DOIs
Publication statusPublished - 5 Aug 2013
Externally publishedYes

Keywords

  • Discontinuous Galerkin
  • Elliptic problems
  • Hybrid formulations
  • Stabilized finite element methods

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