Open Access
Volume 57, Number 3, May-June 2023
Page(s) 1257 - 1296
Published online 12 May 2023
  1. R. Adams and J.F. Fournier, Sobolev Spaces. Vol. 140 of Pure and Applied Mathematics , 2nd edition. Elsevier (2003). [Google Scholar]
  2. M. Ainsworth and G. Fu, Fully computable a posteriori error bounds for hybridizable discontinuous Galerkin finite element approximations. J. Sci. Comput. 77 (2018) 443–466. [Google Scholar]
  3. S. Badia and R. Codina, Unified stabilized finite element formulations for the Stokes and the Darcy problems. SIAM J. Numer. Anal. 47 (2009) 1971–2000. [Google Scholar]
  4. J. Bear and A.H.-D. Cheng, Modeling Groundwater Flow and Contaminant Transport. Vol. 23 of Theory and Applications of Transport in Porous Media. Springer (2010). [Google Scholar]
  5. G.S. Beavers and D.D. Joseph, Boundary conditions at a naturally impermeable wall. J. Fluid. Mech. 30 (1967) 197–207. [Google Scholar]
  6. S.C. Brenner, Poincaré-Friedrichs inequalities for piecewise H1 functions. SIAM J. Numer. Anal. 41 (2003) 306–324. [Google Scholar]
  7. S.C. Brenner, Korn’s inequalities for piecewise H1 vector fields. Math. Comp. 73 (2004) 1067–1087. [Google Scholar]
  8. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods, 3rd edition. Springer (2010). [Google Scholar]
  9. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Vol. 15 of Springer Series in Computational Mathematics. Springer-Verlag, New York Inc. (1991). [Google Scholar]
  10. A.N. Brooks and T.J.R. Hughes, Streamline upwind Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equation. Comput. Meth. Appl. Mech. Eng. 32 (1982) 199–259. [CrossRef] [Google Scholar]
  11. E. Burman and P. Hansbo, Stabilized Crouzeix-Raviart element for the Darcy-Stokes problem. Numer. Meth. Part. D. E. 21 (2005) 986–997. [Google Scholar]
  12. J. Camaño, G.N. Gatica, R. Oyarzúa, R. Ruiz-Baier and P. Venegas, New fully-mixed finite element methods for the Stokes-Darcy coupling. Comput. Method. Appl. M. 295 (2015) 362–395. [CrossRef] [Google Scholar]
  13. Y. Cao, M. Gunzburger, X. Hu, F. Hua, X. Wang and W. Zhao, Finite element approximations for Stokes-Darcy flow with Beavers-Joseph interface conditions. SIAM J. Numer. Anal. 47 (2010) 4239–4256. [Google Scholar]
  14. A. Çeşmelioğlu and B. Rivière, Existence of a weak solution for the fully coupled Navier–Stokes/Darcy–transport problem. J. Differ. Equ. 252 (2012) 4138–4175. [CrossRef] [Google Scholar]
  15. A. Cesmelioglu and P. Chidyagwai, Numerical analysis of the coupling of free fluid with a poroelastic material. Numer. Meth. Part. D. E. 36 (2020) 463–494. [Google Scholar]
  16. A. Cesmelioglu and S. Rhebergen, A compatible embedded-hybridized discontinuous Galerkin method for the Stokes–Darcy-transport problem. Commun. Appl. Math. Comput. 4 (2022) 293–318. [CrossRef] [MathSciNet] [Google Scholar]
  17. A. Cesmelioglu, S. Rhebergen and G.N. Wells, An embedded-hybridized discontinuous Galerkin method for the coupled Stokes-Darcy system. J. Comput. Appl. Math. 367 (2020) 112476. [Google Scholar]
  18. N. Chaabane, V. Girault, C. Puelz and B. Riviere, Convergence of IPDG for coupled time-dependent Navier-Stokes and Darcy equations. J. Comput. Appl. Math. 324 (2017) 25–48. [CrossRef] [MathSciNet] [Google Scholar]
  19. B. Cockburn and C.-W. Shu, The local discontinuous Galerkin finite element method for time-dependent convection–diffusion systems. SIAM J. Numer. Anal. 35 (1998) 2440–2463. [Google Scholar]
  20. B. Cockburn, J. Gopalakrishnan and R. Lazarov, Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems. SIAM J. Numer. Anal. 47 (2009) 1319–1365. [Google Scholar]
  21. C. D’Angelo and P. Zunino, Robust numerical approximation of coupled Stokes’ and Darcy’s flows applied to vascular hemodynamics and biochemical transport. ESAIM: M2AN 45 (2011) 447–476. [CrossRef] [EDP Sciences] [Google Scholar]
  22. C. Dawson, S. Sun and M.F. Wheeler, Compatible algorithms for coupled flow and transport. Comput. Methods Appl. Mech. Eng. 193 (2004) 2565–2580. [CrossRef] [Google Scholar]
  23. D.A. Di Pietro and A. Ern, Mathematical Aspects of Discontinuous GAlerkin Methods. Vol. 69 of Mathématiques et Applications. Springer-Verlag, Berlin Heidelberg (2012). [Google Scholar]
  24. M. Discacciati, Domain decomposition methods for the coupling of surface and groundwater flows. Ph.D. thesis, Ecole Polytechnique Federale de Sausanne, Sausanne, Switzerland (2004). [Google Scholar]
  25. M. Discacciati, E. Miglio and A. Quarteroni, Mathematical and numerical models for coupling surface and groundwater flows. Appl. Numer. Math. 43 (2002) 57–74. [Google Scholar]
  26. J. Douglas Jr., R.E. Ewing and M.F. Wheeler, A time-discretization procedure for a mixed finite element approximation of miscible displacement in porous media. RAIRO. Anal. numér. 17 (1983) 249–265. [Google Scholar]
  27. A. Ern and J.-L. Guermond, Theory and Practice of Finite Elements. Vol. 159 of Applied Mathematical Sciences. Springer-Verlag, New York (2004). [CrossRef] [Google Scholar]
  28. V. Ervin, M. Kubacki, W. Layton, M. Moraiti, Z. Si and C. Trenchea, Partitioned penalty methods for the transport equation in the evolutionary Stokes–Darcy–transport problem. Numer. Meth. Part. D. E. 35 (2019) 349–374. [Google Scholar]
  29. G.N. Gatica, S. Meddahi and R. Oyarzúa, A conforming mixed finite-element method for the coupling of fluid flow with porous media flow. IMA J. Numer. Anal. 29 (2009) 86–108. [Google Scholar]
  30. V. Girault and B. Rivière, DG approximation of coupled Navier-Stokes and Darcy equations by Beaver–Joseph–Saffman interface condition. SIAM J. Numer. Anal. 47 (2009) 2052–2089. [Google Scholar]
  31. J. Guzmán, C.-W. Shu and F. Sequeira, H(div) conforming and DG methods for incompressible Euler’s equations. IMA J. Numer. Anal. 37 (2016) 1733–1771. [Google Scholar]
  32. P. Hansbo and M.G. Larson, Discontinuous Galerkin methods for incompressible and nearly incompressible elasticity by Nitsche’s method. Comput. Methods Appl. Mech. Eng. 191 (2002) 1895–1908. [CrossRef] [Google Scholar]
  33. N. Hanspal, A. Waghode, V. Nassehi and R. Wakeman, Numerical analysis of coupled stokes/darcy flows in industrial filtrations. Transp. Porous Media 64 (2006) 1573–1634. [Google Scholar]
  34. G. Kanschat and B. Rivière, A strongly conservative finite element method for the coupling of Stokes and Darcy flow. J. Comput. Phys. 229 (2010) 5933–5943. [CrossRef] [MathSciNet] [Google Scholar]
  35. W. Layton, Introduction to the Numerical Analysis of Incompressible Viscous Flows. Society for Industrial and Applied Mathematics, Philadelphia, PA (2008). [CrossRef] [Google Scholar]
  36. W. Layton, F. Schieweck and I. Yotov, Coupling fluid flow with porous media flow. SIAM J. Numer. Anal. 40 (2002) 2195–2218. [Google Scholar]
  37. J. Li, B. Riviere and N. Walkington, Convergence of a high order method in time and space for the miscible displacement equations. ESAIM: M2AN 49 (2015) 953–976. [CrossRef] [EDP Sciences] [Google Scholar]
  38. J. Lohrenz, B.G. Bray and C.R. Clark, Calculating viscosities of reservoir fluids from their compositions. J. Petrol. Technol. 16 (1964) 1171–1176. [Google Scholar]
  39. A. Márquez, S. Meddahi and F.J. Sayas, Strong coupling of finite element methods for the Stokes-Darcy problem. IMA J. Numer. Anal. 35 (2015) 969–988. [CrossRef] [MathSciNet] [Google Scholar]
  40. N.C. Nguyen, J. Peraire and B. Cockburn, An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations. J. Comput. Phys. 228 (2009) 3232–3254. [CrossRef] [MathSciNet] [Google Scholar]
  41. B. Rivière, Analysis of a discontinuous finite element method for the coupled Stokes and Darcy problems. J. Sci. Comput. 22 (2005) 479–500. [Google Scholar]
  42. B. Rivière, Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations. Vol. 35 of Frontiers in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM) Philadelphia (2008). [Google Scholar]
  43. B. Riviere, Discontinuous finite element methods for coupled surface–subsurface flow and transport problems, in Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations: 2012 John H Barrett Memorial Lectures, edited by X. Feng, O. Karakashian and Y. Xing. Springer International Publishing, Cham (2014) 259–279. [Google Scholar]
  44. B. Rivière and N.J. Walkington, Convergence of a discontinuous Galerkin method for the miscible displacement equation under low regularity. SIAM J. Numer. Anal. 49 (2011) 1085–1110. [Google Scholar]
  45. H. Rui and J. Zhang, A stabilized mixed finite element method for coupled Stokes and Darcy flows with transport. Comput. Methods Appl. Mech. Eng. 315 (2017) 169–189. [CrossRef] [Google Scholar]
  46. P. Saffman, On the boundary condition at the surface of a porous media. Stud. Appl. Math. 50 (1971) 292–315. [Google Scholar]
  47. J. Schöberl, NETGEN an advancing front 2D/3D-mesh generator based on abstract rules. Comput. Visual. Sci. 1 (1997) 41–52. [CrossRef] [Google Scholar]
  48. J. Schöberl, C++11 implementation of finite elements in NGSolve. Technical Report ASC Report 30/2014, Institute for Analysis and Scientific Computing, Vienna University of Technology (2014). [Google Scholar]
  49. S. Sun, B. Rivière and M.F. Wheeler, A combined mixed finite element and discontinuous Galerkin method for miscible displacement problem in porous media, in Recent Progress in Computational and Applied PDES. Springer US, Boston, MA (2002) 323–351. [Google Scholar]
  50. D. Vassilev and I. Yotov, Coupling Stokes-Darcy flow with transport. SIAM J. Sci. Comput. 31 (2009) 3661–3684. [Google Scholar]
  51. G.N. Wells, Analysis of an interface stabilized finite element method: the advection-diffusion-reaction equation. SIAM J. Numer. Anal. 49(1) (2011) 87–109. [Google Scholar]
  52. J. Zhang, H. Rui and Y. Cao, A partitioned method with different time steps for coupled stokes and darcy flows with transport. Int. J. Numer. Anal. Model. 16 (2019) 463–498. [MathSciNet] [Google Scholar]

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