Numerical Analysis
A posteriori error estimation in the conforming finite element method based on its local conservativity and using local minimization
Comptes Rendus. Mathématique, Volume 346 (2008) no. 11-12, pp. 687-690.

We present in this Note fully computable a posteriori error estimates allowing for accurate error control in the conforming finite element discretization of pure diffusion problems. The derived estimates are based on the local conservativity of the conforming finite element method on a dual grid associated with simplex vertices rather than directly on the Galerkin orthogonality.

Nous présentons dans cette Note des estimations a posteriori entièrement calculables, permettant le contrôle d'erreur dans la discrétisation de problèmes à diffusion pure par la méthode des éléments finis conformes. Ces estimations sont basées sur la conservativité locale de la méthode des éléments finis conformes sur un maillage dual associé aux sommets des triangles ou tétraèdres au lieu de l'orthogonalité de Galerkine.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.03.006
Vohralík, Martin 1, 2

1 UPMC Université Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France
2 CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France
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Vohralík, Martin. A posteriori error estimation in the conforming finite element method based on its local conservativity and using local minimization. Comptes Rendus. Mathématique, Volume 346 (2008) no. 11-12, pp. 687-690. doi : 10.1016/j.crma.2008.03.006. http://www.numdam.org/articles/10.1016/j.crma.2008.03.006/

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[3] I. Cheddadi, R. Fučík, M.I. Prieto, M. Vohralík, Guaranteed and robust a posteriori error estimates for singularly perturbed reaction–diffusion problems, (2008), submitted for publication

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[8] M. Vohralík, Residual flux-based a posteriori error estimates for finite volume discretizations of inhomogeneous, anisotropic, and convection-dominated problems, (2006), submitted for publication

[9] Vohralík, M. A posteriori error estimates for lowest-order mixed finite element discretizations of convection–diffusion–reaction equations, SIAM J. Numer. Anal., Volume 45 (2007) no. 4, pp. 1570-1599

[10] M. Vohralík, Guaranteed and fully robust a posteriori error estimates for conforming discretizations of diffusion problems with discontinuous coefficients, (2008), submitted for publication

Cited by Sources:

This work was supported by the GdR MoMaS project “Numerical Simulations and Mathematical Modeling of Underground Nuclear Waste Disposal”, PACEN/CNRS, ANDRA, BRGM, CEA, EdF, IRSN.