Open Access
Issue
ESAIM: M2AN
Volume 59, Number 3, May-June 2025
Page(s) 1399 - 1435
DOI https://doi.org/10.1051/m2an/2025024
Published online 27 May 2025
  1. S. Averweg, A. Schwarz, C. Schwarz, and J. Schröder. 3d modeling of generalized newtonian fluid flow with data assimilation using the least-squares finite element method. Comput. Methods Appl. Mech. Eng. 392 (2022) 114668. [CrossRef] [Google Scholar]
  2. M. Bachmayr and A. Cohen, Kolmogorov widths and low-rank approximations of parametric elliptic PDEs. Math. Comput. 86 (2017) 701–724. [Google Scholar]
  3. M. Badra, F. Caubet and J. Dardé, Stability estimates for Navier–Stokes equations and application to inverse problems. Discrete Continuous Dyn. Sys. Ser. B 21 (2016) 2379–2407. [CrossRef] [Google Scholar]
  4. A. Ballerini, Stable determination of an immersed body in a stationary Stokes fluid. Inverse Prob. 26 (2010) 125015. [CrossRef] [Google Scholar]
  5. P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova and P. Wojtaszczyk, Data assimilation in reduced modeling. SIAM/ASA J. Uncertain. Quantif. 5 (2017) 1–29. [CrossRef] [MathSciNet] [Google Scholar]
  6. P. Binev, A. Bonito, A. Cohen, W. Dahmen, R. DeVore and G. Petrova, Solving PDEs with incomplete information. SIAM J. Numer. Anal. 62 (2024) 1278–1312. [CrossRef] [MathSciNet] [Google Scholar]
  7. M. Boulakia, A.-C. Egloffe and C. Grandmont, Stability estimates for the unique continuation property of the Stokes system and for an inverse boundary coefficient problem. Inverse Prob. 29 (2013) 115001. [CrossRef] [Google Scholar]
  8. M. Boulakia, E. Burman, M.A. Fernández and C. Voisembert, Data assimilation finite element method for the linearized Navier–Stokes equations in the low reynolds regime. Inverse Prob. 36 (2020) 085003. [CrossRef] [Google Scholar]
  9. 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]
  10. E. Burman and P. Hansbo, Stabilized nonconforming finite element methods for data assimilation in incompressible flows. Math. Comp. 87 (2018) 1029–1050. [Google Scholar]
  11. E. Burman and L. Oksanen, Weakly Consistent Regularisation Methods for Ill-Posed Problems. Springer International Publishing, Cham (2018) 171–202. [Google Scholar]
  12. E. Burman and L. Oksanen, Finite element approximation of unique continuation of functions with finite dimensional trace. Math. Models Methods Appl. Sci. 34 (2024) 1809–1824. [CrossRef] [MathSciNet] [Google Scholar]
  13. 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]
  14. E. Burman, D. Garg and J. Preuss, Data assimilation finite element method for the linearized Navier–Stokes equations with higher order polynomial approximation. ESAIM: Math. Model. Numer. Anal. 58 (2024) 223–245. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  15. A. Cohen and R. DeVore, Kolmogorov widths under holomorphic mappings. IMA J. Numer. Anal. 36 (2016) 1–12. [Google Scholar]
  16. M. D’Elia, M. Perego and A. Veneziani, A variational data assimilation procedure for the incompressible Navier–Stokes equations in hemodynamics. J. Sci. Comput. 52 (2012) 340–359. [CrossRef] [MathSciNet] [Google Scholar]
  17. J. Douglas and T. Dupont, Interior Penalty Procedures for Elliptic and Parabolic Galerkin Methods. Springer Berlin Heidelberg (1976) 207–216. [Google Scholar]
  18. A. Ern and J.-L. Guermond, Theory and Practice of Finite Elements. Springer New York (2004). [CrossRef] [Google Scholar]
  19. C. Fabre and G. Lebeau, Prolongement unique des solutions de l’équation de stokes. Commun. Part. Differ. Equ. 21 (1996) 573–596. [CrossRef] [Google Scholar]
  20. B. García-Archilla and J. Novo, Error analysis of fully discrete mixed finite element data assimilation schemes for the Navier–Stokes equations. Adv. Comput. Math. 46 (2020) 61. [CrossRef] [Google Scholar]
  21. K. Kunisch and S. Volkwein, Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics. SIAM J. Numer. Anal. 40 (2002) 492–515. [CrossRef] [MathSciNet] [Google Scholar]
  22. C.-L. Lin, G. Uhlmann and J.-N. Wang, Optimal three-ball inequalities and quantitative uniqueness for the Stokes system. Discrete Contin. Dyn. Syst. 28 (2010) 1273–1290. [CrossRef] [MathSciNet] [Google Scholar]
  23. Y. Maday, A.T. Patera and G. Turinici, A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations. J. Sci. Comput. 17 (2002) 437–446. [Google Scholar]
  24. N. Parikh and S. Boyd, Proximal algorithms. Found. Trends Optim. 1 (2013) 123–231. [Google Scholar]
  25. F. Shakib, T.J.R. Hughes and Z. Johan, A new finite element formulation for computational fluid dynamics: X. The compressible euler and Navier–Stokes equations. Comput. Methods Appl. Mech. Eng. 89 (1991) 141–219. [CrossRef] [Google Scholar]
  26. R. Temam, On the Theory and Numerical Analysis of the Navier–Stokes Equations. Universite Paris XI (1973). [Google Scholar]
  27. P.R. Turner, Numerical Analysis, Lancaster 1984. Lecture notes in Mathematics, 1985 edition. Springer, Berlin, Germany (1985). [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