An accurate H (div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems

Alexandre Ern; Serge Nicaise; Martin Vohralík

doi:10.1016/j.crma.2007.10.036

An accurate H (div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems

Alexandre Ern
, Serge Nicaise
, Martin Vohralík

Université de Valenciennes et du Hainaut Cambrésis
UPMC Université de Paris VI

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We introduce a new H (div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems. The reconstructed flux is computed elementwise and its divergence equals the L²-orthogonal projection of the source term onto the discrete space. Moreover, the energy-norm of the error in the flux is bounded by the discrete energy-norm of the error in the primal variable, independently of diffusion heterogeneities. To cite this article: A. Ern et al., C. R. Acad. Sci. Paris, Ser. I 345 (2007).

langue originale	Anglais
Pages (de - à)	709-712
Nombre de pages	4
journal	Comptes Rendus Mathematique
Volume	345
Numéro de publication	12
Les DOIs	https://doi.org/10.1016/j.crma.2007.10.036
état	Publié - 15 déc. 2007

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abstract = "We introduce a new H (div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems. The reconstructed flux is computed elementwise and its divergence equals the L2-orthogonal projection of the source term onto the discrete space. Moreover, the energy-norm of the error in the flux is bounded by the discrete energy-norm of the error in the primal variable, independently of diffusion heterogeneities. To cite this article: A. Ern et al., C. R. Acad. Sci. Paris, Ser. I 345 (2007).",

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AU - Nicaise, Serge

AU - Vohralík, Martin

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N2 - We introduce a new H (div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems. The reconstructed flux is computed elementwise and its divergence equals the L2-orthogonal projection of the source term onto the discrete space. Moreover, the energy-norm of the error in the flux is bounded by the discrete energy-norm of the error in the primal variable, independently of diffusion heterogeneities. To cite this article: A. Ern et al., C. R. Acad. Sci. Paris, Ser. I 345 (2007).

AB - We introduce a new H (div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems. The reconstructed flux is computed elementwise and its divergence equals the L2-orthogonal projection of the source term onto the discrete space. Moreover, the energy-norm of the error in the flux is bounded by the discrete energy-norm of the error in the primal variable, independently of diffusion heterogeneities. To cite this article: A. Ern et al., C. R. Acad. Sci. Paris, Ser. I 345 (2007).

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An accurate H (div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems

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