Open Access
Issue
ESAIM: M2AN
Volume 59, Number 3, May-June 2025
Page(s) 1301 - 1331
DOI https://doi.org/10.1051/m2an/2025030
Published online 14 May 2025
  1. A. Bensoussan, Stochastic Navier–Stokes equations. Acta App. Math. 38 (1995) 267–304. [CrossRef] [Google Scholar]
  2. H. Bessaih and A. Millet, Strong convergence of time numerical schemes for the stochastic two-dimensional Navier–Stokes equations. IMA J. Numer. Anal. 39 (2019) 2135–2167. [CrossRef] [MathSciNet] [Google Scholar]
  3. H. Bessaih and A. Millet, Strong rates of convergence of space-time discretization schemes for the 2D Navier–Stokes equations with additive noise. Stoch. Dyn. 22 (2022) 2240005. [CrossRef] [Google Scholar]
  4. H. Bessaih, Z. Brzeźniak and A. Millet, Splitting up method for the 2D stochastic Navier–Stokes equations. Stoch. Part. Differ. Equ. Anal. Comput. 2 (2014) 433–470. [Google Scholar]
  5. D. Breit and A. Dodgson, Convergence rates for the numerical approximation of the 2D stochastic Navier–Stokes equations. Numer. Math. 147 (2021) 553–578. [CrossRef] [MathSciNet] [Google Scholar]
  6. Z. Brzeźniak, On stochastic convolution in Banach spaces and applications. Stoch. Int. J. Probab. Stoch. Process. 61 (1997) 245–295. [Google Scholar]
  7. Z. Brzeźniak, E. Carelli and A. Prohl, Finite-element-based discretizations of the incompressible Navier–Stokes equations with multiplicative random forcing. IMA J. Numer. Anal. 33 (2013) 771–824. [CrossRef] [MathSciNet] [Google Scholar]
  8. E. Carelli and A. Prohl, Rates of convergence for discretizations of the stochastic incompressible Navier–Stokes equations. SIAM J. Numer. Anal. 50 (2012) 2467–2496. [CrossRef] [MathSciNet] [Google Scholar]
  9. E. Carelli, E. Hausenblas and A. Prohl, Time-splitting methods to solve the stochastic incompressible Stokes equation. SIAM J. Numer. Anal. 50 (2012) 2917–2939. [CrossRef] [MathSciNet] [Google Scholar]
  10. P.-L. Chow, Stochastic Partial Differential Equations. Chapman and Hall/CRC (2007). [Google Scholar]
  11. G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions. Vol. 152. Cambridge University Press (2014). [CrossRef] [Google Scholar]
  12. X. Feng and H. Qiu, Analysis of fully discrete mixed finite element methods for time-dependent stochastic Stokes equations with multiplicative noise. J. Sci. Comput. 88 (2021) 31. [CrossRef] [Google Scholar]
  13. X. Feng and L. Vo, Analysis of Chorin-type projection methods for the stochastic Stokes equations with general multiplicative noise, in Stochastics and Partial Differential Equations: Analysis and Computations. Springer (2022) 1–38. [Google Scholar]
  14. X. Feng and L. Vo, High moment and pathwise error estimates for fully discrete mixed finite element approximattions of stochastic Navier–Stokes equations with additive noise. Preprint arXiv:2209.12374 (2022). [Google Scholar]
  15. X. Feng, Y. Li and Y. Zhang, A fully discrete mixed finite element method for the stochastic Cahn–Hilliard equation with gradient-type multiplicative noise. J. Sci. Comput. 83 (2020) 1–24. [CrossRef] [Google Scholar]
  16. X. Feng, A. Prohl and L. Vo, Optimally convergent mixed finite element methods for the stochastic Stokes equations. IMA J. Numer. Anal. 41 (2021) 2280–2310. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. Hairer and J.C. Mattingly, Ergodicity of the 2D Navier–Stokes equations with degenerate stochastic forcing. Ann. Math. 164 (2006) 993–1032. [CrossRef] [MathSciNet] [Google Scholar]
  18. A. Ichikawa, Stability of semilinear stochastic evolution equations. J. Math. Anal. App. 90 (1982) 12–44. [CrossRef] [Google Scholar]
  19. J.A. Langa, J. Real and J. Simon, Existence and regularity of the pressure for the stochastic Navier–Stokes equations. Appl. Math. Optim. 48 (2003) 195–210. [CrossRef] [MathSciNet] [Google Scholar]
  20. B. Li, S. Ma and W. Sun, Optimal analysis of finite element methods for the stochastic Stokes equations. Math. Comput. 94 (2025) 551–583. [Google Scholar]
  21. R. Temam, Navier–Stokes Equations: Theory and Numerical Analysis. Vol. 343. American Mathematical Society (2024). [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