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

By M. V. Raalte, Bram van Leer. Communications in Computational Physics, 2009

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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.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/7ceec35ab1b06cb4a3b104a536f36f3b2f3cfa94

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Local Discontinuous Galerkin Methods for High-Order Time-Dependent Partial Differential Equations (2009, methodology): “More recently, van Leer and Nomura [88] (see also van Raalte and van Leer [89]) and Gassner et al.”