HAL : hal-00383692, version 1

DOI : 10.1137/090759008

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SIAM Journal on Numerical Analysis 48, 1 (2010) 198-223

A posteriori error estimation based on potential and flux reconstruction for the heat equation

Alexandre Ern 1, Martin Vohralik 2

(2010)

We derive a posteriori error estimates for the discretization of the heat equation in a unified and fully discrete setting comprising the discontinuous Galerkin, finite volume, mixed finite element, and conforming and nonconforming finite element methods in space and the backward Euler scheme in time. Our estimates are based on a $H^1$-conforming reconstruction of the potential, continuous and piecewise affine in time, and a locally conservative $H(div)$-conforming reconstruction of the flux, piecewise constant in time. They yield a guaranteed and fully computable upper bound on the error measured in the energy norm augmented by a dual norm of the time derivative. Local-in-time lower bounds are also derived; for nonconforming methods on time-varying meshes, the lower bounds require a mild parabolic-type constraint on the meshsize.

1 :	Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS)
	Ecole des Ponts ParisTech
2 :	Laboratoire Jacques-Louis Lions (LJLL)
	CNRS : UMR7598 – Université Paris VI - Pierre et Marie Curie

Domaine

:

Mathématiques/Analyse numérique

Mots Clés : heat equation – unified framework – a posteriori estimate – nonconforming methods

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Contributeur : Alexandre Ern <>

Soumis le : Mercredi 13 Mai 2009, 11:39:23

Dernière modification le : Mercredi 2 Novembre 2011, 17:30:28