Numerical analysis
Error estimates for stabilized finite element methods applied to ill-posed problems

Presented by: the Editorial Board

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

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.

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.

Received:
Accepted:
Published online:
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, Volume 352 (2014) no. 7-8, pp. 655-659. doi : 10.1016/j.crma.2014.06.008. https://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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