EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 49 / No 5 (September-October 2015) ESAIM: M2AN, 49 5 (2015) 1399-1427 References
Free Access
Issue
ESAIM: M2AN
Volume 49, Number 5, September-October 2015
Page(s) 1399 - 1427
DOI https://doi.org/10.1051/m2an/2015015
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 http://www.ci2ma.udec.cl/publicaciones/prepublicaciones/. [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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you