Free Access
Volume 49, Number 5, September-October 2015
Page(s) 1399 - 1427
Published online 19 August 2015
  1. R.A. Adams and J.J.F. Fournier, Sobolev Spaces. Academic Press. Elsevier Ltd (2003). [Google Scholar]
  2. M. Alvarez, G.N. Gatica and R. Ruiz-Baier, Mixed-primal finite element approximation of a steady sedimentation-consolidation system. In preparation (2015). [Google Scholar]
  3. P.R. Amestoy, I.S. Duff and J.-Y. L’Excellent, Multifrontal parallel distributed symmetric and unsymmetric solvers. Comput. Methods Appl. Mech. Engrg. 184 (2000) 501–520. [Google Scholar]
  4. C. Amrouche, C. Bernardi, M. Dauge and V. Girault, Vector potentials in three-dimensional non-smooth domains. Math. Methods Appl. Sci. 21 (1998) 823–864. [CrossRef] [MathSciNet] [Google Scholar]
  5. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer-Verlag (1991). [Google Scholar]
  6. R. Bürger, R. Ruiz-Baier and H. Torres, A stabilized finite volume element formulation for sedimentation-consolidation processes. SIAM J. Sci. Comput. 34 (2012) B265–B289. [CrossRef] [Google Scholar]
  7. R. Bürger, W.L. Wendland and F. Concha, Model equations for gravitational sedimentation-consolidation processes. ZAMM Z. Angew. Math. Mech. 80 (2000) 79–92. [CrossRef] [MathSciNet] [Google Scholar]
  8. M.C. Bustos, F. Concha, R. Bürger and E.M. Tory, Sedimentation and Thickening. Kluwer Academic Publishers, Dordrecht (1999). [Google Scholar]
  9. Z. Cai, B. Lee and P. Wang, Least-squares methods for incompressible Newtonian fluid flow: linear stationary problems. SIAM J. Numer. Anal. 42 (2004) 843–859. [CrossRef] [Google Scholar]
  10. P. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland (1978). [Google Scholar]
  11. P. Ciarlet, Linear and Nonlinear Functional Analysis with Applications. Society for Industrial and Applied Mathematics, Philadelphia, PA (2013). [Google Scholar]
  12. E. Colmenares, G.N. Gatica and R. Oyarzúa, Analysis of an augmented mixed-primal formulation for the stationary Boussinesq problem. Centro de Investigación en Ingeniería Matemática, Universidad de Concepción, (2014). Preprint 2015-07. Available at [Google Scholar]
  13. C. Cox, H. Lee and D. Szurley, Finite element approximation of the non-isothermal Stokes-Oldroyd equations. Int. J. Numer. Anal. Model. 4 (2007) 425–440. [Google Scholar]
  14. G. de Vahl Davis, Natural convection of air in a square cavity: A benchmark numerical solution. Int. J. Numer. Meth. Fluids 3 (1983) 249–264. [Google Scholar]
  15. M. Farhloul and A. Zine, A dual mixed formulation for non-isothermal Oldroyd-Stokes problem. Math. Model. Nat. Phenom. 6 (2011) 130–156. [Google Scholar]
  16. M. Farhloul, S. Nicaise and L. Paquet, A mixed formulation of Boussinesq equations: Analysis of nonsingular solutions. Math. Comput. 69 (2000) 965–986. [CrossRef] [Google Scholar]
  17. L.E. Figueroa, G.N. Gatica and N. Heuer, A priori and a posteriori error analysis of an augmented mixed finite element method for incompressible fluid flows. Comput. Methods Appl. Mech. Engrg. 198 (2008) 280–291. [CrossRef] [MathSciNet] [Google Scholar]
  18. L.E. Figueroa, G.N. Gatica and A. Márquez, Augmented mixed finite element methods for the stationary Stokes equations. SIAM J. Sci. Comput. 31 (2008/09) 1082–1119. [CrossRef] [Google Scholar]
  19. T. Fusegi and J.M. Hyun, A numerical study of 3D natural convection in a cube: effects of the horizontal thermal boundary conditions. Fluid Dyn. Res. 8 (1991) 221–230. [CrossRef] [Google Scholar]
  20. G.N. Gatica, Analysis of a new augmented mixed finite element method for linear elasticity allowing RT0 − P1 − P0 approximations. ESAIM: M2AN 40 (2006) 1–28. [CrossRef] [EDP Sciences] [Google Scholar]
  21. G.N. Gatica, A Simple Introduction to the Mixed Finite Element Method: Theory and Applications. Springer Briefs in Mathematics. Springer, Cham (2014). [Google Scholar]
  22. G.N. Gatica and G.C. Hsiao, On the coupled BEM and FEM for a nonlinear exterior Dirichlet problem in . Numer. Math. 61 (1992) 171–214. [CrossRef] [MathSciNet] [Google Scholar]
  23. G.N. Gatica and W. Wendland, Coupling of mixed finite elements and boundary elements for linear and nonlinear elliptic problems. Appl. Anal. 63 (1996) 39–75. [CrossRef] [MathSciNet] [Google Scholar]
  24. G.N. Gatica, A. Márquez and M.A. Sánchez, Analysis of a velocity-pressure-pseudostress formulation for the stationary Stokes equations. Comput. Methods Appl. Mech. Engrg. 199 (2010) 1064–1079. [CrossRef] [MathSciNet] [Google Scholar]
  25. G.N. Gatica, R. Oyarzúa and F.-J. Sayas, A twofold saddle point approach for the coupling of fluid flow with nonlinear porous media flow. IMA J. Numer. Anal. 32 (2012) 845–887. [CrossRef] [MathSciNet] [Google Scholar]
  26. Y. Le Pentrec, and G. Lauriat, Effects of the heat transfer at the side walls on natural convection in cavities. J. Heat Trans. 112 (1990) 370–378. [CrossRef] [Google Scholar]
  27. J. Nečas, Introduction to the Theory of Nonlinear Elliptic Equations. Reprint of the 1983 edition. A Wiley-Interscience Publication. John Wiley & Sons, Ltd., Chichester (1986). [Google Scholar]
  28. R. Oyarzúa, T. Qin and D. Schötzau, An exactly divergence-free finite element method for a generalized Boussinesq problem. IMA J. Numer. Anal. 34 (2014) 1104–1135. [CrossRef] [MathSciNet] [Google Scholar]
  29. A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations. Vol. 23 of Springer Ser. Comput. Math. Springer-Verlag Berlin Heidelberg (1994). [Google Scholar]
  30. R. Ruiz-Baier and H. Torres, Numerical solution of a multidimensional sedimentation problem using finite volume-element methods. Appl. Numer. Math. 95 (2015) 280–291. [CrossRef] [Google Scholar]
  31. S.B. Savage, Gravity flow of cohesionless granular materials in chutes and channels. J. Fluid Mech. 92 (1979) 53–96. [CrossRef] [Google Scholar]

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