Open Access
Volume 57, Number 2, March-April 2023
Page(s) 745 - 783
Published online 27 March 2023
  1. B. Andreianov, F. Boyer and F. Hubert, Discrete duality finite volume schemes for Leray-Lions-type elliptic problems on general 2D meshes. Numer. Methods Partial Differ. Equ. 23 (2007) 145–195. [Google Scholar]
  2. R. Anton, D. Cohen and L. Quer-Sardanyons, A fully discrete approximation of the one-dimensional stochastic heat equation. IMA J. Numer. Anal. 40 (2020) 247–284. [Google Scholar]
  3. P. Baldi, Stochastic Calculus. Springer International Publishing, Cham (2017). [Google Scholar]
  4. C. Bauzet and F. Nabet, Convergence of a finite-volume scheme for a heat equation with a multiplicative stochastic force. In Finite volumes for complex applications IX—methods, theoretical aspects, examples, In Vol. 323 of Springer Proceedings in Mathematics and Statistics. Springer, Cham (2020) 275–283. [CrossRef] [Google Scholar]
  5. C. Bauzet, J. Charrier and T. Gallouët, Convergence of flux-splitting finite volume schemes for hyperbolic scalar conservation laws with a multiplicative stochastic perturbation. Math. Comput. 85 (2016) 2777–2813. [Google Scholar]
  6. C. Bauzet, J. Charrier and T. Gallouët, Convergence of monotone finite volume schemes for hyperbolic scalar conservation laws with multiplicative noise. Stoch. Partial Differ. Equ. Anal. Comput. 4 (2016) 150–223. [Google Scholar]
  7. C. Bauzet, J. Charrier and T. Gallouët, Numerical approximation of stochastic conservation laws on bounded domains. ESAIM Math. Model. Numer. Anal. 51 (2017) 225–278. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  8. C. Bauzet, V. Castel and J. Charrier, Existence and uniqueness result for an hyperbolic scalar conservation law with a stochastic force using a finite volume approximation. J. Hyperbolic Differ. Equ. 17 (2020) 213–294. [CrossRef] [MathSciNet] [Google Scholar]
  9. L. Baňas, Z. Brzeźniak, M. Neklyudov and A. Prohl, Stochastic Ferromagnetism, In Vol. 58 of De Gruyter Studies in Mathematics, De Gruyter, Berlin (2014). [Google Scholar]
  10. P. Billingsley, Convergence of probability measures, Wiley Series in Probability and Statistics: Probability and Statistics, 2nd edition. John Wiley & Sons Inc., New York (1999). [Google Scholar]
  11. D. Breit, E. Feireisl and M. Hofmanová, Stochastically forced compressible fluid flows, In Vol. 3 of De Gruyter Series in Applied and Numerical Mathematics. De Gruyter, Berlin (2018). [Google Scholar]
  12. D. Breit, M. Hofmanová and S. Loisel, Space-time approximation of stochastic p-Laplace-type systems. SIAM J. Numer. Anal. 59 (2021) 2218–2236. [Google Scholar]
  13. H. Brézis, Opérateurs Maximaux Monotones. North-Holland Mathematics Studies, North-Holland Publishing Co (1973). [Google Scholar]
  14. H. Brézis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Universitext, Springer, New York (2011). [CrossRef] [Google Scholar]
  15. H. Brézis and E. Lieb, A relation between pointwise convergence of functions and convergence of functionals. Proc. Amer. Math. Soc. 88 (1983) 486–490. [Google Scholar]
  16. G. Da Prato and J. Zabczyk, Stochastic equations in infinite dimensions, In Vol. 152 of Encyclopedia of Mathematics and its Applications, 2nd edition. Cambridge University Press, Cambridge (2014). [Google Scholar]
  17. A. Debussche and J. Printems, Weak order for the discretization of the stochastic heat equation. Math. Comput. 78 (2009) 845–863. [Google Scholar]
  18. A. Debussche, N. Glatt-Holtz and R. Temam, Local martingale and pathwise solutions for an abstract fluids model. Phys. D: Nonlinear Phenom. 240 (2011) 1123–1144. [Google Scholar]
  19. C. Dellacherie and P.-A. Meyer, Probabilités et Potentiel. Chapitres V à VIII. Actualités Scientifiques et Industrielles, No. 1385. Hermann, Paris (1980). [Google Scholar]
  20. J. Diestel and J.J. Uhl, Jr., Vector Measures. Mathematical Surveys, No. 15. American Mathematical Society, Providence, R.I. (1977). [Google Scholar]
  21. S. Dotti and J. Vovelle, Convergence of approximations to stochastic scalar conservations laws. Arch. Ration. Mech. Anal. 1 (2018) 1–53. [Google Scholar]
  22. S. Dotti and J. Vovelle, Convergence of the finite volume method for scalar conservation laws with multiplicative noise: an approach by kinetic formulation. Stoch. Partial Differ. Equ.: Anal. Comput. 8 (2020) 265–310. [Google Scholar]
  23. J. Droniou, Intégration et espaces de Sobolev à valeurs vectorielles. (2001). [Google Scholar]
  24. J. Droniou, A density result in Sobolev spaces. J. Math. Pures App. 81 (2002) 697–714. [Google Scholar]
  25. R. Eymard and T. Gallouët, H-convergence and numerical scheme for elliptic problems. SIAM J. Numer. Anal. 41 (2003) 539–562. [Google Scholar]
  26. R. Eymard, T. Gallouët and R. Herbin, Finite Volume Methods. Handb. Numer. Anal., VII. North-Holland, Amsterdam (2000) 713–1020. [Google Scholar]
  27. F. Flandoli and D. Gatarek, Martingale and stationary solutions for stochastic Navier-Stokes equations. Probab. Theory Relat. Fields 102 (1995). [Google Scholar]
  28. T. Funaki, Y. Gao and D. Hilhorst, Convergence of a finite volume scheme for a stochastic conservation law involving a Q-Brownian motion. Discrete Contin. Dyn. Syst. Ser. B 23 (2018) 1459–1502. [MathSciNet] [Google Scholar]
  29. T. Gallouët, R. Herbin, A. Larcher and J.-C. Latché, Analysis of a fractional-step scheme for the P1 radiative diffusion model. Comput. Appl. Math. 35 (2016) 135–151. [CrossRef] [MathSciNet] [Google Scholar]
  30. I. Gyöngy and N. Krylov, Existence of strong solutions for Itô’s stochastic equations via approximations. Probab. Theory Relat. Fields 105 (1996) 143–158. [Google Scholar]
  31. N.V. Krylov and B.L. Rozovskii, Stochastic evolution equations. J. Sov. Math. 16 (1981) 1233–1277. [Google Scholar]
  32. W. Liu and M. Röckner, Stochastic Partial Differential Equations: An Introduction. Universitext. Springer, Cham (2015). [Google Scholar]
  33. A. Majee, Convergence of a flux-splitting finite volume scheme for conservation laws driven by Lévy noise. Appl. Math. Comput. 338 (2018) 676–697. [MathSciNet] [Google Scholar]
  34. M. Ondrejat, A. Prohl and N. Walkington, Numerical approximation of nonlinear SPDE’s. Stoch. Partial Differ. Equ.: Anal. Comput. (2022) 1–82. [Google Scholar]
  35. É. Pardoux, Équations aux dérivées partielles stochastiques non linéaires monotones. Ph.D. thesis, University Paris Sud (1975). [Google Scholar]
  36. M.M. Rao and R.J. Swift, Probability Theory with Applications. Springer, New York, N.Y. (2006). [Google Scholar]
  37. T. Roubíček, Nonlinear partial differential equations with applications, In Vol. 153 of International Series of Numerical Mathematics, 2nd edition. Birkhäuser/Springer Basel AG, Basel (2013). [Google Scholar]
  38. G. Vallet and A. Zimmermann, Well-posedness for nonlinear SPDEs with strongly continuous perturbation. Proc. Roy. Soc. Edinburgh Sect. A 151 (2021) 265–295. [Google Scholar]

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