Year: 2009
Journal of Computational Mathematics, Vol. 27 (2009), Iss. 6 : pp. 697–712
Abstract
A new recovery operator $P : Q^{disc}_n (\mathcal{T}) → Q^{disc}_{n+1}(\mathcal{M})$ for discontinuous Galerkin is derived. It is based on the idea of projecting a discontinuous, piecewise polynomial solution on a given mesh $\mathcal{T}$ into a higher order polynomial space on a macro mesh $\mathcal{M}$. In order to do so, we define local degrees of freedom using polynomial moments and provide global degrees of freedom on the macro mesh. We prove consistency with respect to the local $L_2$-projection, stability results in several norms and optimal anisotropic error estimates. As an example, we apply this new recovery technique to a stabilized solution of a singularly perturbed convection-diffusion problem using bilinear elements.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2009.09-m2899
Journal of Computational Mathematics, Vol. 27 (2009), Iss. 6 : pp. 697–712
Published online: 2009-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Discontinuous Galerkin Postprocessing Recovery.