Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

Superconvergence of hp-discontinuous Galerkin methods for convection-diffusion problems

Fatih Celiker, Bernardo Cockburn*
University of Minnesota, School of Mathematics, 206 Church St, SE, Minneapolis, MN 55455, USA
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ABSTRACT
We study some superconvergence properties of discontinuous Galerkin methods for convection-diffusion problems in one space dimension. We show that the nodal error converges with order 2p + 1 if polynomials of degree p are used. The theoretical results are verified by numerical experiments.

Keywords:  Superconvergence; Discontinuous Galerkin methods; Postprocessing
* Corresponding author. Tel.: +1 (612) 625 2587; Fax: +1 (612) 626 2017; E-mail: cockburn@math.umn.edu