Some multilevel decoupled algorithms for a mixed navier-stokes/darcy model

[1]  William Layton,et al.  Two-level Picard and modified Picard methods for the Navier-Stokes equations , 1995 .

[2]  Andrew J. Wathen,et al.  A Preconditioner for the Steady-State Navier-Stokes Equations , 2002, SIAM J. Sci. Comput..

[3]  P. Hansbo,et al.  A unified stabilized method for Stokes' and Darcy's equations , 2007 .

[4]  P. Hood,et al.  A numerical solution of the Navier-Stokes equations using the finite element technique , 1973 .

[5]  B. Rivière,et al.  On the solution of the coupled Navier–Stokes and Darcy equations , 2009 .

[6]  G. Burton Sobolev Spaces , 2013 .

[7]  Ivan Yotov,et al.  Coupling Fluid Flow with Porous Media Flow , 2002, SIAM J. Numer. Anal..

[8]  Jinchao Xu,et al.  A Two-Grid Method of a Mixed Stokes-Darcy Model for Coupling Fluid Flow with Porous Media Flow , 2007, SIAM J. Numer. Anal..

[9]  VIVETTE GIRAULT,et al.  DG Approximation of Coupled Navier-Stokes and Darcy Equations by Beaver-Joseph-Saffman Interface Condition , 2009, SIAM J. Numer. Anal..

[10]  Vivette Girault,et al.  Finite Element Methods for Navier-Stokes Equations - Theory and Algorithms , 1986, Springer Series in Computational Mathematics.

[11]  Béatrice Rivière,et al.  Locally Conservative Coupling of Stokes and Darcy Flows , 2005 .

[12]  Lutz Tobiska,et al.  A Two-Level Method with Backtracking for the Navier--Stokes Equations , 1998 .

[13]  Béatrice Rivière,et al.  A two-grid method for coupled free flow with porous media flow , 2011 .

[14]  Santiago Badia,et al.  Unified Stabilized Finite Element Formulations for the Stokes and the Darcy Problems , 2009, SIAM J. Numer. Anal..

[15]  E. Miglio,et al.  Mathematical and numerical models for coupling surface and groundwater flows , 2002 .

[16]  Mingchao Cai Modeling and numerical simulation for the coupling of surface flow with subsurface flow , 2008 .

[17]  Jinchao Xu,et al.  Numerical Solution to a Mixed Navier-Stokes/Darcy Model by the Two-Grid Approach , 2009, SIAM J. Numer. Anal..

[18]  William Layton,et al.  A two-level discretization method for the Navier-Stokes equations , 1993 .

[19]  Barry Smith,et al.  Domain Decomposition Methods for Partial Differential Equations , 1997 .

[20]  Jinru Chen,et al.  Two-level and multilevel methods for Stokes-Darcy problem discretized by nonconforming elements on nonmatching meshes , 2012 .

[21]  Vincent J. Ervin,et al.  Approximation of the Stokes–Darcy System by Optimization , 2014, J. Sci. Comput..

[22]  Huang Pei Two-level and multilevel methods for Stokes-Darcy problem discretized by nonconforming elements on nonmatching meshes , 2012 .

[23]  Shuyu Sun,et al.  Coupled Generalized Nonlinear Stokes Flow with Flow through a Porous Medium , 2009, SIAM J. Numer. Anal..

[24]  Mingchao Cai,et al.  A multilevel decoupled method for a mixed Stokes/Darcy model , 2012, J. Comput. Appl. Math..

[25]  Xiaoliang Cheng,et al.  A two-grid method based on Newton iteration for the Navier-Stokes equations , 2008 .

[26]  Alfio Quarteroni,et al.  Domain Decomposition Methods for Compressible Flows , 1999 .

[27]  Yanren Hou,et al.  Optimal error estimates of a decoupled scheme based on two-grid finite element for mixed Stokes-Darcy model , 2015, Appl. Math. Lett..

[28]  P. Saffman On the Boundary Condition at the Surface of a Porous Medium , 1971 .

[29]  Willi Jäger,et al.  On The Interface Boundary Condition of Beavers, Joseph, and Saffman , 2000, SIAM J. Appl. Math..

[30]  H. K. Lee,et al.  Numerical Solution of the Stationary Navier-Stokes Equations Using a Multilevel Finite Element Method , 1998, SIAM J. Sci. Comput..

[31]  Tong Zhang,et al.  Two novel decoupling algorithms for the steady Stokes-Darcy model based on two-grid discretizations , 2014 .

[32]  Fédérale De Lausanne,et al.  DOMAIN DECOMPOSITION METHODS FOR THE COUPLING OF SURFACE AND GROUNDWATER FLOWS , 2004 .

[33]  Alfio Quarteroni,et al.  Robin-Robin Domain Decomposition Methods for the Stokes-Darcy Coupling , 2007, SIAM J. Numer. Anal..

[34]  Jinchao Xu,et al.  Preconditioning techniques for a mixed Stokes/Darcy model in porous media applications , 2009, J. Comput. Appl. Math..

[35]  Jinchao Xu Two-grid Discretization Techniques for Linear and Nonlinear PDEs , 1996 .

[36]  D. Joseph,et al.  Boundary conditions at a naturally permeable wall , 1967, Journal of Fluid Mechanics.

[37]  William Layton,et al.  A multilevel mesh independence principle for the Navier-Stokes equations , 1996 .

[38]  Andro Mikelico,et al.  ON THE INTERFACE BOUNDARY CONDITION OF , 2000 .

[39]  Yanren Hou,et al.  A decoupling two‐grid algorithm for the mixed Stokes‐Darcy model with the Beavers‐Joseph interface condition , 2014 .

[40]  M. Cai Decoupled Algorithms for the Coupled Surface /Subsurface Flow Interaction Problems , 2012 .

[41]  Yanren Hou,et al.  Numerical analysis for the mixed Navier–Stokes and Darcy Problem with the Beavers–Joseph interface condition , 2015 .

[42]  A. Quarteroni,et al.  Convergence analysis of a subdomain iterative method for the finite element approximation of the coupling of Stokes and Darcy equations , 2004 .

[43]  Mingchao Cai,et al.  A Newton type linearization based two grid method for coupling fluid flow with porous media flow , 2016 .

[44]  Alfio Quarteroni,et al.  Numerical analysis of the Navier–Stokes/Darcy coupling , 2010, Numerische Mathematik.

[45]  Weidong Zhao,et al.  Finite Element Approximations for Stokes–darcy Flow with Beavers–joseph Interface Conditions * , 2022 .

[46]  Michel Fortin,et al.  Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.