no. 7-8
Numerical analysis
Error estimates for stabilized finite element methods applied to ill-posed problems
[Estimations d'erreurs pour des méthodes d'éléments finis stabilisées appliquées à des problèmes mal posés]

Présenté par : the Editorial Board

Burman, Erik1
1 Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, United Kingdom
Comptes Rendus. Mathématique, Tome 352 (2014) no. 7-8, pp. 655-659.

Dans cette note, nous proposons une nouvelle analyse pour les méthodes d'éléments finis stabilisées introduites dans Burman (2013) [2], appliquées a des problèmes mal posés avec des propriétés de dépendance continue faibles. Nous obtenons des estimations a priori et a posteriori sans supposer ni coercitivité ni stabilité inf–sup de la forme bilinéaire du problème continu.

We propose an analysis for the stabilized finite element methods proposed in Burman (2013) [2] valid in the case of ill-posed problems for which only weak continuous dependence can be assumed. A priori and a posteriori error estimates are obtained without assuming coercivity or inf–sup stability of the continuous problem.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.06.008
Burman, Erik 1

1 Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, United Kingdom 
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Burman, Erik. Error estimates for stabilized finite element methods applied to ill-posed problems. Comptes Rendus. Mathématique, Tome 352 (2014) no. 7-8, pp. 655-659. doi : 10.1016/j.crma.2014.06.008. http://www.numdam.org/articles/10.1016/j.crma.2014.06.008/

[1] Alessandrini, G.; Rondi, L.; Rosset, E.; Vessella, S. The stability for the Cauchy problem for elliptic equations, Inverse Probl., Volume 25 (2009) no. 12, p. 123004 (47 p)

[2] Burman, E. Stabilized finite element methods for nonsymmetric, noncoercive, and ill-posed problems. Part I: Elliptic equations, SIAM J. Sci. Comput., Volume 35 (2013) no. 6, p. A2752-A2780

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