Bilinear Forms for the Recovery-Based Discontinuous Galerkin Method for Diffusion

Bilinear Forms for the Recovery-Based Discontinuous Galerkin Method for Diffusion

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

Keywords: