EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 56 / No 6 (November-December 2022) ESAIM: M2AN, 56 6 (2022) 2021-2050 References
Open Access
Issue
ESAIM: M2AN
Volume 56, Number 6, November-December 2022
Page(s) 2021 - 2050
DOI https://doi.org/10.1051/m2an/2022061
Published online 14 September 2022
  1. F. Ben Belgacem, Why is the Cauchy problem severely ill-posed? Inverse Prob. 23 (2007) 823–836. [CrossRef] [Google Scholar]
  2. A. Bensoussan, Sur l’identification et le filtrage de systèmes gouvernés par des équations aux dérivées partielles. Cahier/Institut de Recherche d’Informatique et d’Automatique. IRIA (1969). [Google Scholar]
  3. L. Bourgeois, A mixed formulation of quasi-reversibility to solve the Cauchy problem for Laplace’s equation. Inverse Prob. 21 (2005) 1087–1104. [CrossRef] [Google Scholar]
  4. L. Bourgeois, Convergence rates for the quasi-reversibility method to solve the cauchy problem for laplace’s equation. Inverse Prob. 22 (2006) 413–430. [CrossRef] [Google Scholar]
  5. L. Bourgeois and L. Chesnel, On quasi-reversibility solutions to the cauchy problem for the laplace equation: regularity and error estimates. ESAIM: M2AN 54 (2020) 493–529. [CrossRef] [EDP Sciences] [Google Scholar]
  6. L. Bourgeois and J. Dardé, A duality-based method of quasi-reversibility to solve the Cauchy problem in the presence of noisy data. Inverse Prob. 26 (2010) 095016. [CrossRef] [Google Scholar]
  7. L. Bourgeois and J. Dardé, A quasi-reversibility approach to solve the inverse obstacle problem. Inverse Prob. Imaging 4 (2010) 351–377. [CrossRef] [Google Scholar]
  8. L. Bourgeois and A. Recoquillay, A mixed formulation of the Tikhonov regularization and its application to inverse PDE problems. ESAIM: M2AN 52 (2018) 123–145. [CrossRef] [EDP Sciences] [Google Scholar]
  9. E. Burman and L. Oksanen, Data assimilation for the heat equation using stabilized finite element methods. Numer. Math. 139 (2018) 505–528. [Google Scholar]
  10. E. Burman, P. Hansbo and M.G. Larson, Solving ill-posed control problems by stabilized finite element methods: an alternative to Tikhonov regularization. Inverse Prob. 34 (2018) 035004. [CrossRef] [Google Scholar]
  11. E. Burman, A. Feizmohammadi, A. Münch and L. Oksanen, Space time stabilized finite element methods for a unique continuation problem subject to the wave equation. ESAIM: M2AN 55 (2021) S969–S991. [CrossRef] [EDP Sciences] [Google Scholar]
  12. F. Caubet and J. Dardé, A dual approach to Kohn–Vogelius regularization applied to data completion problem. Inverse Prob. 36 (2020) 065008. [CrossRef] [Google Scholar]
  13. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. Vol. 4. Studies in Mathematics and its Applications. North-Holland Publishing Co., Amsterdam-New York-Oxford (1978). [Google Scholar]
  14. N. Cndea and A. Münch, Inverse problems for linear hyperbolic equations using mixed formulations. Inverse Prob. 31 (2015) 075001. [CrossRef] [Google Scholar]
  15. N. Cîndea, A. Imperiale and P. Moireau, Data assimilation of time under-sampled measurements using observers, the wave-like equation example. ESAIM: COCV 21 (2015) 635–669. [CrossRef] [EDP Sciences] [Google Scholar]
  16. P. Demeestère, A remark on the relation between the tykhonov regularization and constraint relaxation for an optimal control problem. Appl. Math. Lett. 11 (1998) 85–89. [CrossRef] [MathSciNet] [Google Scholar]
  17. I. Ekeland and R. Temam, Convex Analysis and Variational Problems. SIAM (1999). [Google Scholar]
  18. S. Ervedoza, Control issues and linear projection constraints on the control and on the controlled trajectory. North-West. Eur. J. Math. 6 (2020) 165–197. [MathSciNet] [Google Scholar]
  19. F. Hecht, New development in freefem++. J. Numer. Math. 20 (2012) 251–265. [Google Scholar]
  20. A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems. Vol. 120, Springer Nature (2021). [CrossRef] [Google Scholar]
  21. R. Lattès and J.-L. Lions, Méthode de quasi-réversibilité et applications. Travaux et Recherches Mathématiques, No. 15. Dunod, Paris (1967). [Google Scholar]
  22. K. Law, A. Stuart and K. Zygalakis, Data Assimilation. Vol. 214. Springer (2015). [CrossRef] [Google Scholar]
  23. G. Lebeau and L. Robbiano, Contrôle exact de l’équation de la chaleur Commun. Part. Differ. Equ. 20 (1995) 335–356. [CrossRef] [Google Scholar]
  24. J.-L. Lions, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués: Contrôlabilité exacte. Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. Masson (1988). [Google Scholar]
  25. J.L. Lions, Remarks on approximate controllability. J. d’Analyse Math. 59 (1992) 103–116. [CrossRef] [MathSciNet] [Google Scholar]
  26. A. Osses and J.P. Puel, On the controllability of the laplace equation observed on an interior curve. Rev. Mat. Complut. 11 (1998) 403. [CrossRef] [MathSciNet] [Google Scholar]
  27. J.P. Zubelli, V. Albani and A. De Cezaro, On the choice of the tikhonov regularization parameter and the discretization level: a discrepancy-based strategy. Inverse Prob. Imaging 10 (2016) 1–25. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you