Open Access
Volume 57, Number 3, May-June 2023
Page(s) 1143 - 1170
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]

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