Skip Navigation



IMA Journal of Numerical Analysis Advance Access published online on July 10, 2009
IMA Journal of Numerical Analysis, doi:10.1093/imanum/drn083
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Egger, H.
Right arrow Articles by Schöberl, J.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A hybrid mixed discontinuous Galerkin finite-element method for convection–diffusion problems

Herbert Egger{dagger} and Joachim Schöberl

Centre for Computational Engineering Science, RWTH Aachen University, Aachen, Germany

{dagger} Corresponding author. Email: herbert.egger{at}rwth-aachen.de

Received on 15 March 2008. Accepted for publication 8 November 2008.


  Abstract

We propose and analyse a new finite-element method for convection–diffusion problems based on the combination of a mixed method for the elliptic and a discontinuous Galerkin (DG) method for the hyperbolic part of the problem. The two methods are made compatible via hybridization and the combination of both is appropriate for the solution of intermediate convection–diffusion problems. By construction, the discrete solutions obtained for the limiting subproblems coincide with the ones obtained by the mixed method for the elliptic and the DG method for the limiting hyperbolic problem. We present a new type of analysis that explicitly takes into account the Lagrange multipliers introduced by hybridization. The use of adequate energy norms allows us to treat the purely diffusive, the convection-dominated and the hyperbolic regimes in a unified manner. In numerical tests we illustrate the efficiency of our approach and make a comparison with results obtained using other methods for convection–diffusion problems.

Key Words: convection–diffusion; upwind; finite-element method; discontinuous Galerkin methods; mixed methods; hybridization


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.