@Article{CiCP-5-683,
author = {Marc van Raalte and Bram van Leer},
title = {Bilinear Forms for the Recovery-Based Discontinuous Galerkin Method for Diffusion},
journal = {Communications in Computational Physics},
year = {2009},
volume = {5},
number = {2-4},
pages = {683--693},
abstract = {<p style="text-align: justify;">The present paper introduces bilinear forms that are equivalent to the recovery-based discontinuous Galerkin formulation introduced by Van Leer in 2005. The recovery method approximates the solution of the diffusion equation in a discontinuous function space, while inter-element coupling is achieved by a local L<sub>2</sub> projection that recovers a smooth continuous function underlying the discontinuous approximation. Here we introduce the concept of a local “recovery polynomial basis” – smooth polynomials that are in the weak sense indistinguishable from the discontinuous basis polynomials – and show it allows us to eliminate the recovery procedure. The recovery method reproduces the symmetric discontinuous Galerkin formulation with additional penalty-like terms depending on the targeted accuracy of the method. We present the unique link between the recovery method and discontinuous Galerkin bilinear forms.&nbsp;</p>},
issn = {1991-7120},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/cicp/7757.html}
}