Free Access
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
Page(s) S417 - S445
Published online 26 February 2021
  1. C. Amrouche and N.E.H. Seloula, Lp-theory for vector potentials and Sobolev’s inequalities for vector fields: application to the Stokes equations with pressure boundary conditions. Math. Models Methods Appl. Sci. 23 (2013) 37–92. [Google Scholar]
  2. M. Bessemoulin-Chatard and A. Jüngel, A finite volume scheme for a Keller-Segel model with additional cross-diffusion. IMA J. Numer. Anal. 34 (2014) 96–122. [Google Scholar]
  3. G. Chamoun, M. Saad and R. Talhouk, Numerical analysis of a chemotaxis-swimming bacteria model on a general triangular mesh. Appl. Numer. Math. 127 (2018) 324–348. [Google Scholar]
  4. A. Chertock, K. Fellner, A. Kurganov, A. Lorz and P. Markowich, Sinking, merging and stationary plumes in a coupled chemotaxis-fluid model: a high-resolution numerical approach. J. Fluid Mech. 694 (2012) 155–190. [Google Scholar]
  5. M. Cui, Analysis of a semidiscrete discontinuous Galerkin scheme for compressible miscible displacement problem. J. Comput. Appl. Math. 214 (2008) 617–636. [Google Scholar]
  6. Y. Deleuze, C.-Y. Chiang, M. Thiriet and T.W. Sheu, Numerical study of plume patterns in a chemotaxis-diffusion-convection coupling system. Comput. Fluids 126 (2016) 58–70. [Google Scholar]
  7. J. Douglas, Jr. and J.E. Roberts, Numerical methods for a model for compressible miscible displacement in porous media. Math. Comput. 41 (1983) 441–459. [Google Scholar]
  8. A. Duarte-Rodríguez, L.C.F. Ferreira and E.J. Villamizar-Roa, Global existence for an attraction-repulsion chemotaxis fluid model with logistic source. Disc. Contin. Dyn. Syst. Ser. B 24 (2019) 423–447. [Google Scholar]
  9. Y. Epshteyn and A. Izmirlioglu, Fully discrete analysis of a discontinuous finite element method for the Keller-Segel chemotaxis model. J. Sci. Comput. 40 (2009) 211–256. [Google Scholar]
  10. F. Filbet, A finite volume scheme for the Patlak–Keller–Segel chemotaxis model. Numer. Math. 104 (2006) 457–488. [Google Scholar]
  11. V. Girault and P.-A. Raviart, Finite Element Methods for Navier–Stokes Equations. Theory and Algorithms. Springer-Verlag (1986). [Google Scholar]
  12. F. Guillén-González and M.V. Redondo-Neble, Spatial error estimates for a finite element viscosity-splitting scheme for the Navier-Stokes equations. Int. J. Numer. Anal. Model. 10 (2013) 826–844. [Google Scholar]
  13. F. Guillén-González, M.A. Rodrguez-Bellido and D.A. Rueda-Gómez, Unconditionally energy stable fully discrete schemes for a chemo-repulsion model. Math. Comput. 88 (2019) 2069–2099. [Google Scholar]
  14. F. Guillén-González, M.A. Rodrguez-Bellido and D.A. Rueda-Gómez, Study of a chemo-repulsion model with quadratic production. Part I: analysis of the continuous problem and time-discrete numerical schemes. Comput. Math. App. 80 (2020) 692–713. [Google Scholar]
  15. F. Guillén-González, M.A. Rodrguez-Bellido and D.A. Rueda-Gómez, Study of a chemo-repulsion model with quadratic production. Part II: analysis of an unconditionally energy-stable fully discrete scheme. Comput. Math. App. 80 (2020) 636–652. [Google Scholar]
  16. J. Heywood and R. Rannacher, Finite element approximation of the nonstationary Navier-Stokes problem. IV. Error analysis for second order time discretization. SIAM J. Numer. Anal. 27 (1990) 353–384. [Google Scholar]
  17. N. Hill and T. Pedley, Bioconvection. Fluid Dyn. Res. 37 (2005) 1–20. [Google Scholar]
  18. J. Jiang, H. Wu and S. Zheng, Global existence and asymptotic behavior of solutions to a chemotaxis-fluid system on general bounded domains. Asympt. Anal. 92 (2015) 249–258. [Google Scholar]
  19. A. Karimi and M. Paul, Bioconvection in spatially extended domains. Phys. Rev. E 87 (2013) 53016. [Google Scholar]
  20. J. Lankeit, Long-term behaviour in a chemotaxis-fluid system with logistic source. Math. Models Methods Appl. Sci. 26 (2016) 2071–2109. [Google Scholar]
  21. H.G. Lee and J. Kim, Numerical investigation of falling bacterial plumes caused by bioconvection in a three-dimensional chamber. Eur. J. Mech. B/Fluids 52 (2015) 120–130. [Google Scholar]
  22. A. Lorz, Coupled Keller-Segel Stokes model: global existence for small initial data and blow-up delay. Commun. Math. Sci. 10 (2012) 555–574. [Google Scholar]
  23. A. Marrocco, Numerical simulation of chemotactic bacteria aggregation via mixed finite elements. ESAIM: M2AN 37 (2003) 617–630. [EDP Sciences] [Google Scholar]
  24. N. Mizoguchi and P. Souplet, Nondegeneracy of blow-up points for the parabolic Keller-Segel system. Ann. Inst. Henri Poincaré Non Linéaire Anal. 31 (2014) 851–875. [Google Scholar]
  25. J. Necas, Les Méthodes Directes en Théorie des Equations Elliptiques. Editeurs Academia, Prague (1967). [Google Scholar]
  26. N. Saito, Conservative upwind finite-element method for a simplified Keller-Segel system modelling chemotaxis. IMA J. Numer. Anal. 27 (2007) 332–365. [Google Scholar]
  27. N. Saito, Error analysis of a conservative finite-element approximation for the Keller-Segel system of chemotaxis. Commun. Pure Appl. Anal. 11 (2012) 339–364. [CrossRef] [Google Scholar]
  28. R. Stenberg, A technique for analysing finite element methods for viscous incompressible flow. Int. J. Numer. Methods Fluids 11 (1990) 935–948. [Google Scholar]
  29. Y. Tao and M. Winkler, Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis-fluid system. Z. Angew. Math. Phys. 66 (2015) 2555–2573. [Google Scholar]
  30. I. Tuval, L. Cisneros, C. Dombrowski, C.W. Wolgemuth, J.O. Kessler and R.E. Goldstein, Bacterial swimming and oxygen transport near contact lines. Proc. Nat. Acad. Sci. USA 102 (2005) 2277–2282. [Google Scholar]
  31. M. Winkler, Global large-data solutions in a chemotaxis-(Navier–)Stokes system modelling cellular swimming in fluid drops. Commun. Part. Differ. Equ. 37 (2012) 319–351. [Google Scholar]
  32. M. Winkler, Stabilization in a two-dimensional chemotaxis-Navier–Stokes system. Arch. Ration. Mech. Anal. 211 (2014) 455–487. [Google Scholar]
  33. M. Winkler, Global weak solutions in a three-dimensional chemotaxis-Navier–Stokes system. Ann. Inst. Henri Poincaré (C) Non Linear Anal. 33 (2016) 1329–1352. [Google Scholar]
  34. J. Yang and Y. Chen, Superconvergence of a combined mixed finite element and discontinuous Galerkin method for a compressible miscible displacement problem. Acta Math. Appl. Sin. Eng. Ser. 27 (2011) 481–494. [Google Scholar]
  35. Q. Zhang and Y. Li, Convergence rates of solutions for a two-dimensional chemotaxis-Navier–Stokes system. Disc. Contin. Dyn. Syst. Ser. B 20 (2015) 2751–2759. [Google Scholar]
  36. J. Zhang, J. Zhu and R. Zhang, Characteristic splitting mixed finite element analysis of Keller-Segel chemotaxis models. Appl. Math. Comput. 278 (2016) 33–44. [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