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The second-order two-scale computation for integrated heat transfer problem with conduction, convection and radiation in periodic porous materials
Two novel decoupling algorithms for the steady Stokes-Darcy model based on two-grid discretizations
1. | School of Mathematics & Information Science, Henan Polytechnic University, Jiaozuo, 454003, China |
2. | Departamento de Matemática, Universidade Federal do Paraná, Centro Politécnico, Curitiba 81531-980, Brazil |
References:
[1] |
T. Arbogast and D. S. Brunson, A computational method for approximating a Darcy-Stokes system governing a vuggy porous medium, Comput. Geosci., 11 (2007), 207-218.
doi: 10.1007/s10596-007-9043-0. |
[2] |
O. Axelsson and I. E. Kaporin, Minimum residual adaptive multilevel finite element procedure for the solution of nonlinear stationary problems, SIAM J. Numer. Anal., 35 (1998), 1213-1229.
doi: 10.1137/S0036142995286428. |
[3] |
O. Axelsson and W. Layton, A two-level method for the discretization of nonlinear boundary value problems, SIAM J. Numer. Anal., 33 (1996), 2359-2374.
doi: 10.1137/S0036142993247104. |
[4] |
O. Axelsson and A. Padiy, On a two level Newton type procedure applied for solving nonlinear elasticity problems, Internat. J. Numer. Methods Engrg., 49 (2000), 1479-1493.
doi: 10.1002/1097-0207(20001230)49:12<1479::AID-NME4>3.0.CO;2-4. |
[5] |
G. Beavers and D. Josephn, Boundary conditions at a naturally permeable wall, J. Fluid Mech., 30 (1967), 197-207.
doi: 10.1017/S0022112067001375. |
[6] |
F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, 1991.
doi: 10.1007/978-1-4612-3172-1. |
[7] |
M. C. Cai and M. Mu, A multilevel decoupled method for a mixed Stokes/Darcy model, J. Comput. Appl. Math., 236 (2012), 2452-2465.
doi: 10.1016/j.cam.2011.12.003. |
[8] |
M. Discacciati and A. Quarteroni, Convergence analysis of a subdomain iterative method for the finite element approximation of the coupling of Stokes and Darcy equations, Comput. Vis. Sci., 6 (2004), 93-103.
doi: 10.1007/s00791-003-0113-0. |
[9] |
M. Discacciati, E. Miglio and A. Quarteroni, Mathematical and numerical models for coupling surface and groundwater flows, Appl. Numer. Math., 43 (2002), 57-74.
doi: 10.1016/S0168-9274(02)00125-3. |
[10] |
W. Jager and A. Mikelic, On the boundary conditions at the contact interface between a porous medium and a free fluid, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 23 (1996), 403-465. |
[11] |
Y. N. He and K. Liu, A Multi-level Finite element method in space-time for the Navier-Stokes equations, Numer. Methods Partial Differential Eq., 21 (2005), 1052-1078.
doi: 10.1002/num.20077. |
[12] |
Y. N. He, Two-level method based on finite element and Crank-Nicolson extrapolation for the time-dependent Navier-Stokes equations, SIAM J. Numer. Anal., 41 (2003), 1263-1285.
doi: 10.1137/S0036142901385659. |
[13] |
W. Layton and W. Lenferink, Two-level Picard and modified Picard methods for the Navier-Stokes equations, Appl. Math. Comput., 69 (1995), 263-274.
doi: 10.1016/0096-3003(94)00134-P. |
[14] |
W. Layton, A. Meir and P. Schmidt, A two-level discretization method for the stationary MHD equations, Electron. Trans. Numer. Anal., 6 (1997), 198-210. |
[15] |
W. Layton and L. Tobiska, A two-level method with backtracking for the Navier-Stokes equations, SIAM J. Numer. Anal., 35 (1998), 2035-2054.
doi: 10.1137/S003614299630230X. |
[16] |
W. Layton, F. Schieweck and I. Yotov, Coupling fluid flow with porous media flow, SIAM J. Numer. Anal., 40 (2002), 2195-2218.
doi: 10.1137/S0036142901392766. |
[17] |
M. Mu and J. C. Xu, A two-grid method of a mixed Stokes-Darcy model for coupling fluid flow with porous media flow, SIAM J. Numer. Anal., 45 (2007), 1801-1813.
doi: 10.1137/050637820. |
[18] |
J. C. Xu, A novel two-grid method for semilinear elliptic equations, SIAM J. Sci. Comput., 15 (1994), 231-237.
doi: 10.1137/0915016. |
[19] |
J. C. Xu, Two-grid discretization techniques for linear and nonlinear PDEs, SIAM J. Numer. Anal., 33 (1996), 1759-1777.
doi: 10.1137/S0036142992232949. |
[20] |
T. Zhang, Two-grid characteristic finite volume methods for nonlinear parabolic problems, J. Comput. Math., 31 (2013), 470-487.
doi: 10.4208/jcm.1304-m4288. |
[21] |
T. Zhang and S. W. Xu, Two-level stabilized finite volume methods for the stationary Navier-Stokes equations, Adv. Appl. Math. Mech., 5 (2013), 19-35. |
show all references
References:
[1] |
T. Arbogast and D. S. Brunson, A computational method for approximating a Darcy-Stokes system governing a vuggy porous medium, Comput. Geosci., 11 (2007), 207-218.
doi: 10.1007/s10596-007-9043-0. |
[2] |
O. Axelsson and I. E. Kaporin, Minimum residual adaptive multilevel finite element procedure for the solution of nonlinear stationary problems, SIAM J. Numer. Anal., 35 (1998), 1213-1229.
doi: 10.1137/S0036142995286428. |
[3] |
O. Axelsson and W. Layton, A two-level method for the discretization of nonlinear boundary value problems, SIAM J. Numer. Anal., 33 (1996), 2359-2374.
doi: 10.1137/S0036142993247104. |
[4] |
O. Axelsson and A. Padiy, On a two level Newton type procedure applied for solving nonlinear elasticity problems, Internat. J. Numer. Methods Engrg., 49 (2000), 1479-1493.
doi: 10.1002/1097-0207(20001230)49:12<1479::AID-NME4>3.0.CO;2-4. |
[5] |
G. Beavers and D. Josephn, Boundary conditions at a naturally permeable wall, J. Fluid Mech., 30 (1967), 197-207.
doi: 10.1017/S0022112067001375. |
[6] |
F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, 1991.
doi: 10.1007/978-1-4612-3172-1. |
[7] |
M. C. Cai and M. Mu, A multilevel decoupled method for a mixed Stokes/Darcy model, J. Comput. Appl. Math., 236 (2012), 2452-2465.
doi: 10.1016/j.cam.2011.12.003. |
[8] |
M. Discacciati and A. Quarteroni, Convergence analysis of a subdomain iterative method for the finite element approximation of the coupling of Stokes and Darcy equations, Comput. Vis. Sci., 6 (2004), 93-103.
doi: 10.1007/s00791-003-0113-0. |
[9] |
M. Discacciati, E. Miglio and A. Quarteroni, Mathematical and numerical models for coupling surface and groundwater flows, Appl. Numer. Math., 43 (2002), 57-74.
doi: 10.1016/S0168-9274(02)00125-3. |
[10] |
W. Jager and A. Mikelic, On the boundary conditions at the contact interface between a porous medium and a free fluid, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 23 (1996), 403-465. |
[11] |
Y. N. He and K. Liu, A Multi-level Finite element method in space-time for the Navier-Stokes equations, Numer. Methods Partial Differential Eq., 21 (2005), 1052-1078.
doi: 10.1002/num.20077. |
[12] |
Y. N. He, Two-level method based on finite element and Crank-Nicolson extrapolation for the time-dependent Navier-Stokes equations, SIAM J. Numer. Anal., 41 (2003), 1263-1285.
doi: 10.1137/S0036142901385659. |
[13] |
W. Layton and W. Lenferink, Two-level Picard and modified Picard methods for the Navier-Stokes equations, Appl. Math. Comput., 69 (1995), 263-274.
doi: 10.1016/0096-3003(94)00134-P. |
[14] |
W. Layton, A. Meir and P. Schmidt, A two-level discretization method for the stationary MHD equations, Electron. Trans. Numer. Anal., 6 (1997), 198-210. |
[15] |
W. Layton and L. Tobiska, A two-level method with backtracking for the Navier-Stokes equations, SIAM J. Numer. Anal., 35 (1998), 2035-2054.
doi: 10.1137/S003614299630230X. |
[16] |
W. Layton, F. Schieweck and I. Yotov, Coupling fluid flow with porous media flow, SIAM J. Numer. Anal., 40 (2002), 2195-2218.
doi: 10.1137/S0036142901392766. |
[17] |
M. Mu and J. C. Xu, A two-grid method of a mixed Stokes-Darcy model for coupling fluid flow with porous media flow, SIAM J. Numer. Anal., 45 (2007), 1801-1813.
doi: 10.1137/050637820. |
[18] |
J. C. Xu, A novel two-grid method for semilinear elliptic equations, SIAM J. Sci. Comput., 15 (1994), 231-237.
doi: 10.1137/0915016. |
[19] |
J. C. Xu, Two-grid discretization techniques for linear and nonlinear PDEs, SIAM J. Numer. Anal., 33 (1996), 1759-1777.
doi: 10.1137/S0036142992232949. |
[20] |
T. Zhang, Two-grid characteristic finite volume methods for nonlinear parabolic problems, J. Comput. Math., 31 (2013), 470-487.
doi: 10.4208/jcm.1304-m4288. |
[21] |
T. Zhang and S. W. Xu, Two-level stabilized finite volume methods for the stationary Navier-Stokes equations, Adv. Appl. Math. Mech., 5 (2013), 19-35. |
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