Abstract
In this paper, a two-grid method with backtracking is proposed and investigated for the mixed Stokes/Darcy system which describes a fluid flow coupled with a porous media flow. Based on the classical two-grid method [15], a coarse mesh correction is carried out to derive optimal error bounds for the velocity field and the piezometric head in L2 norm. Finally, results of numerical experiments are provided to support the theoretical results.
Funding statement: This work is subsidized by NSFC(Grant No.11701343, 11801332) and Natural Science Foundation of Shandong Province (Grant No. ZR2019BA002, ZR2017BA027).
References
[1] Y. Boubendir and S. Tlupova, Domain decomposition methods for solving Stokes–Darcy problems with boundary integrals, SIAM J. Sci. Comput., 35 (2013), B82–B106.10.1137/110838376Suche in Google Scholar
[2] M. Cai and M. Mu, A multilevel decoupled method for a mixed Stokes/Darcy model, J. Comput. Appl. Math., 236 (2012), 2452–2465.10.1016/j.cam.2011.12.003Suche in Google Scholar
[3] W. Chen, M. Gunzburger, X. He, and X. Wang, Parallel, non-iterative, multi-physics domain decomposition methods for time-dependent Stokes–Darcy systems, Math. Comp., 83 (2014), 1617–1644.10.1090/S0025-5718-2014-02779-8Suche in Google Scholar
[4] 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. Visual Sci., 6 (2004), 93–103.10.1007/s00791-003-0113-0Suche in Google Scholar
[5] M. Discacciati, A. Quarteroni, and A. Valli, Robin–Robin domain decomposition methods for the Stokes–Darcy coupling, SIAM J. Numer. Anal., 45 (2007), 1246–1268.10.1137/06065091XSuche in Google Scholar
[6] G. Du, Y. Hou, and L. Zuo, A modified local and parallel finite element method for the mixed Stokes–Darcy model, J. Math. Anal. Appl., 435 (2016), 1129–1145.10.1016/j.jmaa.2015.11.003Suche in Google Scholar
[7] G. Du and L. Zuo, Local and parallel finite element method for the mixed Navier–Stokes/Darcy model with Beavers–Joseph interface conditions, Acta Math. Sci., 37 (2017), 1331–1347.10.1016/S0252-9602(17)30076-0Suche in Google Scholar
[8] P. Hessari and B. Shin, First order system least squares pseudo-spectral method for Stokes–Darcy equations, Appl. Numer. Math., 120 (2017), 35–52.10.1016/j.apnum.2017.04.010Suche in Google Scholar
[9] Y. Hou, Optimal error estimates of a decoupled scheme based on two-grid finite element for mixed Stokes–Darcy model, Appl. Math. Letters, 57 (2016), 90–96.10.1016/j.aml.2016.01.007Suche in Google Scholar
[10] Y. Hou and Y. Qin, On the solution of coupled Stokes/Darcy model with Beavers–Joseph interface condition, Comput. Math. Appl., 77 (2019), 50–65.10.1016/j.camwa.2018.09.011Suche in Google Scholar
[11] W. Layton, F. Schieweck, and I. Yotov, Coupling fluid flow with porous media flow, SIAM J. Numer. Anal., 40 (2003), 2195–2218.10.1137/S0036142901392766Suche in Google Scholar
[12] Y. Li and Y. Hou, A second-order artificial compression method for the evolutionary Stokes–Darcy system, Numer. Algorithms, (2019), https://doi.org/10.1007/s11075-019-00791-xSuche in Google Scholar
[13] A. Marquez, S. Meddahi, and F. Sayas, A decoupled preconditioning technique for a mixed Stokes–Darcy model, J. Sci. Comput., 57 (2013), 174–192.10.1007/s10915-013-9700-5Suche in Google Scholar
[14] M. Mu and X. Zhu, Decoupled schemes for a non-stationary mixed Stokes–Darcy model, Math. Comput., 79 (2010), 707–731.10.1090/S0025-5718-09-02302-3Suche in Google Scholar
[15] M. Mu and J. 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), 1801–1813.10.1137/050637820Suche in Google Scholar
[16] Y. Qin and Y. Hou, Optimal error estimates of a decoupled scheme based on two-grid finite element for mixed Navier–Stokes/Darcy model, Acta Math. Sci., 38B (2018), 1361–1369.10.1016/S0252-9602(18)30819-1Suche in Google Scholar
[17] L. Shan and H. Zheng, Partitioned time stepping method for fully evolutionary Stokes–Darcy flow with the Beavers–Joseph interface conditions, SIAM J. Numer. Anal., 51 (2013), 813–839.10.1137/110828095Suche in Google Scholar
[18] L. Shan, H. Zheng, and W. Layton, A decoupling method with different subdomain time steps for the nonstationary Stokes–Darcy model, Numer. Meth. Part. D. E., 29 (2013), 549–583.10.1002/num.21720Suche in Google Scholar
[19] L. Zuo and G. Du, A multi-grid technique for coupling fluid flow with porous media flow, Comput. Math. Appl., 75 (2018), 4012–4021.10.1016/j.camwa.2018.03.010Suche in Google Scholar
[20] L. Zuo and G. Du, A parallel two-grid linearized method for the coupled Navier–Stokes–Darcy problem, Numer. Algorithms, 77 (2018), 151–165.10.1007/s11075-017-0308-ySuche in Google Scholar
[21] L. Zuo and G. Du, A multi-grid decoupling method for the coupled fluid flow with the porous media flow, J. Math. Fluid. Mech., 20 (2018), 683–695.10.1007/s00021-017-0340-7Suche in Google Scholar
[22] F. Hecht, New development in FreeFem++. J. Numer. Math., 20 (2012), 251–265.10.1515/jnum-2012-0013Suche in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Boundary update via resolvent for fluid–structure interaction
- Convergence of time-splitting approximations for degenerate convection–diffusion equations with a random source
- A two-grid method with backtracking for the mixed Stokes/Darcy model
- A note on the efficient evaluation of a modified Hilbert transformation
- Collocated finite-volume method for the incompressible Navier–Stokes problem
Artikel in diesem Heft
- Frontmatter
- Boundary update via resolvent for fluid–structure interaction
- Convergence of time-splitting approximations for degenerate convection–diffusion equations with a random source
- A two-grid method with backtracking for the mixed Stokes/Darcy model
- A note on the efficient evaluation of a modified Hilbert transformation
- Collocated finite-volume method for the incompressible Navier–Stokes problem