Jiangshan WANG
,
Lingxiong MENG
,
Xiaofeng JIA
,
Hongen JIA
. NUMERICAL ANALYSIS OF A BDF2 MODULAR GRAD-DIV STABILITY METHOD FOR THE STOKES/DARCY EQUATIONS[J]. Acta mathematica scientia, Series B, 2022
, 42(5)
: 1981
-2000
.
DOI: 10.1007/s10473-022-0515-z
[1] He X, Li J, Lin Y, Ming J. A domain decomposition method for the steady-state Navier-Stokes-Darcy model with Beavers-Joseph-interface condition. SIAM J Sci Comput, 2015, 37(5): 264–290
[2] Zhao J, Zhang T. Two-grid finite element methods for the steady Navier-Stokes/Darcy model. East Asian J Applied Math, 2016, 6(1): 60–79
[3] Qin Y, Hou Y. Optimal error estimates of a decoupled scheme based on two-grid finite element for mixed Navier-Stokes/Darcy model. Acta Math Sci, 2018, 38B: 1361–1369
[4] Jia H, Jia H, Huang Y. A modified two-grid decoupling method for the mixed Navier-Stokes/Darcy Model. Comput Math Appl, 2016, 72(4): 1142–1152
[5] Jia X, Li J, Jia J. Decoupled characteristic stabilized finite element method for time-dependent Navier-Stokes/Darcy model. Numer Methods Partial Differ Equ, 2019, 35(1): 267–294
[6] Cao Y, Gunzburger M, Hu X, Hua F, Wang X, Zhao W. Finite element approximation for Stokes-Darcy flow with Beavers-Joseph interface conditions. SIAM J Numer Anal, 2010, 47(6): 4239–4256
[7] Cui M, Yan N. A posteriori error estimate for the Stokes-Darcy system. Math Methods Appl Sci, 2011, 34(9): 1050–1064
[8] Rui H, Zhang R. A unified stabilized mixed finite element method for coupling Stokes and Darcy flows. Comput Methods Appl Mech Eng, 2009, 198(33): 2692–2699
[9] Jenkins E W, John V, Linke A, Rebholz L G. On the parameter choice in grad-div stabilization for the Stokes equations. Adv Comput Math, 2014, 40(2): 491–516
[10] Olshanskii M, Lube G, Heister T, Löwe J. Grad-div stabilization and subgrid pressure models for the incompressible Navier-Stokes equations. Comput Methods Appl Mech Eng, 2009, 198(49): 3975–3988
[11] Franca L P, Hughes T J R. Two classes of mixed finite element methods. Comput Methods Appl Mech Eng, 1988, 69(1): 89–129
[12] John V, Linke A, Merdon C, Neilan M, Rebholz L G. On the divergence constraint in mixed finite element methods for incompressible flows. SIAM Rev, 2017, 59(3): 492–544
[13] de Frutos J, García-Archilla B, John V, Novo J. Analysis of the grad-div stabilization for the time-dependent Navier-Stokes equations with inf-sup stable finite elements. Adv Comput Math, 2018, 44(1): 195–225
[14] Linke A, Rebholz L G. On a reduced sparsity stabilization of grad-div type for incompressible flow problems. Comput Methods Appl Mech Eng, 2013, 261(15): 142–153
[15] Galvin K J, Linke A, Rebholz L G, Wilson N E. Stabilizing poor mass conservation in incompressible flow problems with large irrotational forcing and application to thermal convection. Comput Methods Appl Mech Eng, 2012, 237: 166–176
[16] Oden JT, Glowinski R, Tallec P L. Augmented Lagrangian and operator-splitting methods in nonlinear mechanics. Math Comput, 1992, 58(197): 451–452.
[17] Jenkins E W, John V, Linke A, Rebholz L G. On the parameter choice in grad-div stabilization for the Stokes equations. Adv Comput Math, 2014, 40(2): 491–516
[18] Fiordilino J A, Layton W, Rong Y. An efficient and modular grad-div stabilization. Comput Methods Appl Mech Engrg, 2018, 335: 327–346
[19] Rong Y, Fiordilino J A. Numerical analysis of a bdf2 modular grad-div Stabilization method for the Navier-Stokes equations. J Sci Comput, 2020, 82(3): 1–22
[20] Qin Y, Hou Y, Huang P, Wang Y. Numerical analysis of two grad-div stabilization methods for the time-dependent Stokes/Darcy model. Comput Math with Appl, 2020, 79(3): 817–832
[21] Jia X, Tang Z, Feng H. Numerical analysis of CNLF modular Grad-Div stabilization method for time-dependent Navier-Stokes equations. Appl Math Lett, 2021, 112: Art 106798
[22] Wei L, Jilin F, Yi Q, Pengzhan H. Rotational pressure-correction method for the Stokes/Darcy model based on the modular grad-div stabilization-ScienceDirect. Appl Numer Math, 2021, 160: 451–465
[23] Akbas M, Rebholz L G. Modular grad-div stabilization for the incompressible non-isothermal fluid flows. Appl Math Comput, 2021, 393: Art 125748
[24] Cesmelioglu A, Riviere B. Analysis of time-dependent Navier-Stokes flow coupled with Darcy flow. J Numer Math, 2008, 16(4): 249–280
[25] Heywood J G, Rannacher R. Finite-element approximation of the nonstationary Navier-Stokes problem part IV: error analysis for second-order time discretization. SIAM J Numer Anal, 1990, 27(2): 353–384
[26] Rong Y, Hou Y. A partitioned second-order method for magnetohydrodynamic flows at small magnetic reynolds numbers. Numer Methods Partial Differ Equ, 2017, 33(6): 1966–1986
[27] Shan L, Zheng H, Layton W. A decoupling method with different subdomain time steps for the nonstationary stokes-darcy model. Numer Methods Partial Differ Equ, 2013, 29(2): 549–583
[28] Kubacki M. Uncoupling evolutionary groundwater-surface water flows using the Crank-Nicolson Leapfrog method. Numer Methods Partial Differ Equ, 2013, 29(4): 1192–121
[29] Hecht F. New development in FreeFEM++. J Numer Math, 2012, 20: 251–265
[30] Layton W. Introduction to the Numerical Analysis of Incompressible, Viscous Flows. SIAM, 2008
