EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 59 / No 5 (September-October 2025) ESAIM: M2AN, 59 5 (2025) 2385-2413 References
Open Access
Issue
ESAIM: M2AN
Volume 59, Number 5, September-October 2025
Page(s) 2385 - 2413
DOI https://doi.org/10.1051/m2an/2025060
Published online 17 September 2025
  1. G. Alessandrini, L. Rondi, E. Rosset and S. Vessella, The stability for the Cauchy problem for elliptic equations. Inverse Probl. 25 (2009) 123004. [CrossRef] [Google Scholar]
  2. L. Bourgeois, A mixed formulation of quasi-reversibility to solve the Cauchy problem for Laplace’s equation. Inverse Probl. 21 (2005) 1087–1104. [Google Scholar]
  3. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York (2011). [Google Scholar]
  4. E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive, and ill-posed problems. Part I: elliptic equations. SIAM J. Sci. Comput. 35 (2013) A2752–A2780. [Google Scholar]
  5. E. Burman, Error estimates for stabilized finite element methods applied to ill-posed problems. C. R. Math. Acad. Sci. Paris 352 (2014) 655–659. [Google Scholar]
  6. E. Burman, P. Hansbo and M.G. Larson, Solving ill-posed control problems by stabilized finite element methods: an alternative to tikhonov regularization. Inverse Probl. 34 (2018) 035004. [Google Scholar]
  7. E. Burman, M. Nechita and L. Oksanen, Unique continuation for the Helmholtz equation using stabilized finite element methods. J. Math. Pures Appl. 129 (2019) 1–22. [Google Scholar]
  8. E. Burman, M. Nechita and L. Oksanen, A stabilized finite element method for inverse problems subject to the convection-diffusion equation. I: diffusion-dominated regime. Numer. Math. 144 (2020) 451–477. [CrossRef] [MathSciNet] [Google Scholar]
  9. P. Ciarlet Jr., Analysis of the Scott-Zhang interpolation in the fractional order Sobolev spaces. J. Numer. Math. 21 (2013) 173–180. [MathSciNet] [Google Scholar]
  10. W. Dahmen, H. Monsuur and R. Stevenson, Least squares solvers for ill-posed PDEs that are conditionally stable. ESAIM: M2AN 57 (2023) 2227–2255. [Google Scholar]
  11. D.A. Di Pietro and A. Ern, Mathematical Aspects of Discontinuous Galerkin Methods. Vol. 69 of Mathématiques & Applications (Berlin) [Mathematics & Applications]. Springer, Heidelberg (2012). [Google Scholar]
  12. D. Dos Santos Ferreira, C.E. Kenig, M. Salo and G. Uhlmann, Limiting Carleman weights and anisotropic inverse problems. Invent. Math. 178 (2009) 119–171. [Google Scholar]
  13. H.W. Engl, M. Hanke and A. Neubauer, Regularization of Inverse Problems. Vol. 375 of Mathematics and its Applications. Kluwer Academic Publishers Group, Dordrecht (1996). [Google Scholar]
  14. A. Ern and J.-L. Guermond, Evaluation of the condition number in linear systems arising in finite element approximations. ESAIM: M2AN 40 (2006) 29–48. [CrossRef] [EDP Sciences] [Google Scholar]
  15. A. Ern and J.-L. Guermond, Finite Elements I – Approximation and Interpolation. Vol. 72 of Texts in Applied Mathematics. Springer, Cham (2021). [Google Scholar]
  16. G.B. Folland, Real Analysis: Modern Techniques and Their Applications. Vol. 40. John Wiley & Sons (1999). [Google Scholar]
  17. F. John, Continuous dependence on data for solutions of partial differential equations with a prescribed bound. Commun. Pure Appl. Math. 13 (1960) 551–585. [CrossRef] [Google Scholar]
  18. J. Le Rousseau and G. Lebeau, On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations. ESAIM Control Optim. Calc. Var. 18 (2012) 712–747. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  19. J.M. Melenk, On Generalized Finite-Element Methods. University of Maryland, College Park (1995). [Google Scholar]
  20. H. Monsuur and R. Stevenson, Ultra-weak least squares discretizations for unique continuation and Cauchy problems. SIAM J. Numer. Anal. 63 (2025) 1344–1368. [Google Scholar]
  21. M. Nechita, Unique continuation problems and stabilised finite element methods. Ph.D. Thesis, University of London, University College London (United Kingdom). ProQuest LLC, Ann Arbor, MI (2020). [Google Scholar]
  22. M. Zworski, Semiclassical Analysis. Vol. 138 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI (2012). [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