EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 57 / No 3 (May-June 2023) ESAIM: M2AN, 57 3 (2023) 1143-1170 References
Open Access
Issue
ESAIM: M2AN
Volume 57, Number 3, May-June 2023
Page(s) 1143 - 1170
DOI https://doi.org/10.1051/m2an/2023007
Published online 08 May 2023
  1. S. Berrone and M. Marro, Space-time adaptive simulations for unsteady Navier-Stokes problems. Comput. Fluids 38 (2009) 1132–1144. [CrossRef] [MathSciNet] [Google Scholar]
  2. C. Canuto and A. Quarteroni, Approximation results for orthogonal polynomials in sobolev spaces. Math. Comput. 38 (1982) 67–86. [Google Scholar]
  3. W. Chen, X. Wang, Y. Yan and Z. Zhang, A second order BDF numerical scheme with variable steps for the Cahn-Hilliard equation. SIAM J. Numer. Anal. 57 (2019) 495–525. [Google Scholar]
  4. M.O. Deville, P.F. Fischer and E.H. Mund, High-Order Methods for Incompressible Fluid Flow. Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press (2002). [Google Scholar]
  5. Y. Di, R. Li, T. Tang and P. Zhang, Moving mesh finite element methods for the incompressible Navier-Stokes equations. SIAM J. Sci. Comput. 26 (2005) 1036–1056. [CrossRef] [MathSciNet] [Google Scholar]
  6. L. Failer and T. Wick, Adaptive time-step control for nonlinear fluid-structure interaction. J. Comput. Phys. 366 (2018) 448–477. [CrossRef] [MathSciNet] [Google Scholar]
  7. V. Girault and P.A. Raviart, Finite Element Approximation of the Navier-Stokes Equations. Springer, Berlin, Heidelberg (1979). [CrossRef] [Google Scholar]
  8. R. Glowinski, Finite element methods for incompressible viscous flow. Handb. Numer. Anal. 9 (2003) 3–1176. [Google Scholar]
  9. M.D. Gunzburger, Finite Element Methods for Viscous Incompressible Flows: A Guide to Theory, Practice, and Algorithms. Computer Science and Scientific Computing. Elsevier, San Diego (1989). [Google Scholar]
  10. A. Hay, S. Etienne, A. Garon and D. Pelletier, Time-integration for ALEsimulations of fluid-structure interaction problems: stepsize and order selection based on the BDF. Comput. Methods Appl. Mech. Eng. 295 (2015) 172–195. [CrossRef] [Google Scholar]
  11. F. Huang and J. Shen, Stability and error analysis of a class of high-order IMEX schemes for Navier-Stokes equations with periodic boundary conditions. SIAM J. Numer. Anal. 59 (2021) 2926–2954. [CrossRef] [MathSciNet] [Google Scholar]
  12. G. Jannoun, E. Hachem, J. Veysset and T. Coupez, Anisotropic meshing with time-stepping control for unsteady convection-dominated problems. Appl. Math. Modell. 39 (2015) 1899–1916. [CrossRef] [Google Scholar]
  13. D.A. Kay, P.M. Gresho, D. Griffiths and D.J. Silvester, Adaptive time-stepping for incompressible flow. Part II: Navier-Stokes equations. SIAM J. Sci. Comput. 32 (2010) 111–128. [CrossRef] [MathSciNet] [Google Scholar]
  14. H. Liao, T. Tang and T. Zhou, On energy stable, maximum-principle preserving, second-order BDF scheme with variable steps for the Allen-Cahn equation. SIAM J. Numer. Anal. 58 (2020) 2294–2314. [CrossRef] [MathSciNet] [Google Scholar]
  15. H. Liao, X. Song, T. Tang and T. Zhou, Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection. Sci. China Math. 64 (2021) 887–902. [CrossRef] [MathSciNet] [Google Scholar]
  16. H. Liao, B. Ji and L. Zhang, An adaptive BDF2 implicit time-stepping method for the phase field crystal model. IMA J. Numer. Anal. 42 (2022) 649–679. [CrossRef] [MathSciNet] [Google Scholar]
  17. J. Liu and R.L. Pego, Stable discretization of magnetohydrodynamics in bounded domains. Commun. Math. Sci. 8 (2010) 235–251. [CrossRef] [MathSciNet] [Google Scholar]
  18. Y. Ma, J. Zhang and C. Zhao, The unconditionally optimal H1-norm error estimate of a semi-implicit galerkin FEMs VSBDF2 scheme for solving semilinear parabolic equations. Preprint (2022). [Google Scholar]
  19. P. Moin and K. Mahesh, Direct numerical simulation: a tool in turbulence research. Ann. Rev. Fluid Mech. 30 (1998) 539–578. [CrossRef] [Google Scholar]
  20. S.A. Orszag and G.S. Patterson, Numerical simulation of three-dimensional homogeneous isotropic turbulence. Phys. Rev. Lett. 28 (1972) 76–79. [CrossRef] [Google Scholar]
  21. R. Peyret, Spectral Methods for Incompressible Viscous Flow. Springer (2002). [CrossRef] [Google Scholar]
  22. Z. Qiao, Z. Zhang and T. Tang, An adaptive time-stepping strategy for the molecular beam epitaxy models. SIAM J. Sci. Comput. 33 (2011) 1395–1414. [CrossRef] [MathSciNet] [Google Scholar]
  23. Z. Qiao, Z. Sun and Z. Zhang, The stability and convergence of two linearized finite difference schemes for the nonlinear epitaxial growth model. Numer. Methods Part. Differ. Equ. 28 (2012) 1893–1915. [CrossRef] [Google Scholar]
  24. Z. She, E. Jackson and S.A. Orszag, Structure and dynamics of homogeneous turbulence: models and simulations. Proc. R. Soc. London. Ser. A: Math. Phys. Sci. 434 (1991) 101–124. [Google Scholar]
  25. R. Temam, Navier-Stokes Equations and Nonlinear Functional Analysis. SIAM, Philadelphia (1982). [Google Scholar]
  26. W. Wang, Y. Chen and H. Fang, On the variable two-step imex BDF method for parabolic integro-differential equations with nonsmooth initial data arising in finance. SIAM J. Numer. Anal. 57 (2019) 1289–1217. [CrossRef] [MathSciNet] [Google Scholar]
  27. W. Wang, M. Mao and Z. Wang, Stability and error estimates for the variable step-size BDF2 method for linear and semilinear parabolic equations. Adv. Comput. Math. 47 (2021) 1–28. [CrossRef] [Google Scholar]
  28. W. Wang, Z. Wang and M. Mao, Linearly implicit variable step-size BDF schemes with fourier pseudospectral approximation for incompressible Navier-Stokes equations. Appl. Numer. Math. 172 (2022) 393–412. [CrossRef] [MathSciNet] [Google Scholar]
  29. K. Wu, F. Huang and J. Shen, A new class of higher-order decoupled schemes for the incompressible Navier-Stokes equations and applications to rotating dynamics. J. Comput. Phys. 458 (2022) 16. [Google Scholar]
  30. J. Zhang and C. Zhao, Sharp error estimate of BDF2 scheme with variable time steps for linear reaction-diffusion equations. J. Math. 41 (2021) 471–488. [MathSciNet] [Google Scholar]
  31. C. Zhao, L. Liu, Y. Ma and J. Zhang, Unconditionally optimal error estimate of a linearized variable-time-step BDF2 scheme for nonlinear parabolic equations. Preprint: arxiv:2201.06008 (2022). [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