Year: 2009
Communications in Computational Physics, Vol. 5 (2009), Iss. 2-4 : pp. 683–693
Abstract
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 L2 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-CiCP-7757
Communications in Computational Physics, Vol. 5 (2009), Iss. 2-4 : pp. 683–693
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11