TY - JOUR
T1 - Bilinear Forms for the Recovery-Based Discontinuous Galerkin Method for Diffusion
AU - Marc van Raalte & Bram van Leer
JO - Communications in Computational Physics
VL - 2-4
SP - 683
EP - 693
PY - 2009
DA - 2009/02
SN - 5
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cicp/7757.html
KW - 
AB - <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>