Volume 5, Issue 2-4
Bilinear Forms for the Recovery-Based Discontinuous Galerkin Method for Diffusion

Marc van Raalte & Bram van Leer

Commun. Comput. Phys., 5 (2009), pp. 683-693.

Published online: 2009-02

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  • 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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@Article{CiCP-5-683, author = {}, 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 = {

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. 

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7757.html} }
TY - JOUR T1 - Bilinear Forms for the Recovery-Based Discontinuous Galerkin Method for Diffusion 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 -

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. 

Marc van Raalte & Bram van Leer. (2020). Bilinear Forms for the Recovery-Based Discontinuous Galerkin Method for Diffusion. Communications in Computational Physics. 5 (2-4). 683-693. doi:
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