Free Access
Volume 49, Number 3, May-June 2015
Page(s) 855 - 874
Published online 16 April 2015
  1. N. Abdellatif and C. Bernardi, A new formulation of the Stokes problem in a cylinder, and its spectral discretization. ESAIM: M2AN 38 (2004) 781–810. [CrossRef] [EDP Sciences] [Google Scholar]
  2. N. Abdellatif, N. Chorfi and S. Trabelsi, Spectral discretization of the axisymmetric vorticity, velocity and pressure formulation of the Stokes problem. J. Sci. Comput. 47 (2011) 419–440. [CrossRef] [Google Scholar]
  3. M. Amara, D. Capatina-Papaghiuc, B. Denel and P. Terpolilli, Mixed finite element approximation for a coupled petroleum reservoir model. ESAIM: M2AN 39 (2005) 349–376. [CrossRef] [EDP Sciences] [Google Scholar]
  4. V. Anaya, D. Mora and R. Ruiz-Baier, An augmented mixed finite element method for the vorticity-velocity-pressure formulation of the Stokes equations. Comput. Methods Appl. Mech. Engrg. 267 (2013) 261–274. [CrossRef] [MathSciNet] [Google Scholar]
  5. V. Anaya, D. Mora, G.N. Gatica and R. Ruiz-Baier, An augmented velocity-vorticity-pressure formulation for the Brinkman problem. To appear in Int. J. Numer. Methods Fluids (2015). [Google Scholar]
  6. V. Anaya, D. Mora, R. Oyarzúa and R. Ruiz-Baier, A priori and a posteriori error analysis for a vorticity-based mixed formulation of the generalized Stokes equations. CI2MA preprint 2014-20. Available from [Google Scholar]
  7. S.M. Aouadi, C. Bernardi and J. Satouri, Mortar spectral element discretization of the Stokes problem in axisymmetric domains. Numer. Methods Partial Differ. Eq. 30 (2014) 44–73. [CrossRef] [Google Scholar]
  8. F. Assous, P. Ciarlet and S. Labrunie,Theoretical tools to solve the axisymmetric Maxwell equations. Math. Methods Appl. Sci. 25 (2002) 49–78. [CrossRef] [Google Scholar]
  9. F. Assous, P. Ciarlet, S. Labrunie and J. Segré, Numerical solution to the time-dependent Maxwell equations in axisymmetric singular domains: the singular complement method. J. Comput. Phys. 191 (2003) 147–176. [CrossRef] [Google Scholar]
  10. M. Azaiez, A spectral element projection scheme for incompressible flow with application to the unsteady axisymmetric Stokes problem. J. Sci. Comput. 17 (2002) 573–584. [CrossRef] [Google Scholar]
  11. G.R. Barrenechea and F. Valentin, An unusual stabilized finite element method for a generalized Stokes problem. Numer. Math. 92 (2002) 653–677. [CrossRef] [MathSciNet] [Google Scholar]
  12. T. Barrios, R. Bustinza, G. García and E. Hernández, On stabilized mixed methods for generalized Stokes problem based on the velocity-pseudostress formulation: a priori error estimates. Comput. Methods Appl. Mech. Engrg. 237/240 (2012) 78–87. [CrossRef] [Google Scholar]
  13. Z. Belhachmi, C. Bernardi and S. Deparis, Weighted Clément operator and application to the finite element discretization of the axisymmetric Stokes problem. Numer. Math. 105 (2002) 217–247. [CrossRef] [MathSciNet] [Google Scholar]
  14. Z. Belhachmi, C. Bernardi, S. Deparis and F. Hecht, An efficient discretization of the Navier-Stokes equations in an axisymmetric domain. Part 1: The discrete problem and its numerical analysis. J. Sci. Comput. 27 (2006) 97–110. [CrossRef] [Google Scholar]
  15. A. Bermúdez, C. Reales, R. Rodríguez and P. Salgado, Numerical analysis of a finite element method for the axisymmetric eddy current model of an induction furnace. IMA J. Numer. Anal. 30 (2010) 654–676. [CrossRef] [MathSciNet] [Google Scholar]
  16. A. Bermúdez, C. Reales, R. Rodríguez and P. Salgado, Mathematical and numerical analysis of a transient eddy current axisymmetric problem involving velocity terms. Numer. Methods Partial Differ. Eq. 28 (2012) 984–1012. [CrossRef] [Google Scholar]
  17. C. Bernardi and N. Chorfi, Spectral discretization of the vorticity, velocity, and pressure formulation of the Stokes problem. SIAM J. Numer. Anal. 44 (2007) 826–850. [CrossRef] [MathSciNet] [Google Scholar]
  18. C. Bernardi, M. Dauge and Y. Maday,Spectral Methods for Axisymmetric Domains. Gauthier-Villars, Éditions Scientifiques et Médicales Elsevier, Paris (1999). [Google Scholar]
  19. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer Verlag, New York (1991). [Google Scholar]
  20. R. Bürger, S. Kumar and R. Ruiz-Baier, Discontinuous finite volume element approximation for a fully coupled Stokes flow-transport problem. CI2MA preprint 2014-25. Available from [Google Scholar]
  21. 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]
  22. J.H. Carneiro de Araujo and V. Ruas, A stable finite element method for the axisymmetric three-field Stokes system. Comput. Methods Appl. Mech. Engrg. 164 (1998) 267–286. [CrossRef] [MathSciNet] [Google Scholar]
  23. P. Clément, Approximation by finite element functions using local regularisation. RAIRO Modél. Math. Anal. Numér. 9 (1975) 77–84. [Google Scholar]
  24. D.M. Copeland, J. Gopalakrishnan and M. Oh, Multigrid in a weighted space arising from axisymmetric electromagnetics. Math. Comput. 79 (2010) 2033–2058. [CrossRef] [Google Scholar]
  25. V.J. Ervin, Approximation of axisymmetric Darcy flow using mixed finite element methods. SIAM J. Numer. Anal. 51 (2013) 1421–1442. [CrossRef] [Google Scholar]
  26. V.J. Ervin, Approximation of coupled Stokes-Darcy flow in an axisymmetric domain. Comput. Methods Appl. Mech. Engrg. 258 (2013) 96–108. [CrossRef] [MathSciNet] [Google Scholar]
  27. G.N. Gatica, A Simple Introduction to the Mixed Finite Element Method. Theory and Applications. Springer Briefs in Mathematics. Springer, Cham, Heidelberg, New York, Dordrecht London (2014). [Google Scholar]
  28. G.N. Gatica, A. Márquez, R. Oyarzúa and R. Rebolledo, Analysis of an augmented fully-mixed approach for the coupling of quasi-Newtonian fluids and porous media. Comput. Methods Appl. Mech. Engrg. 270 (2014) 76–112. [CrossRef] [MathSciNet] [Google Scholar]
  29. G.N. Gatica, L.F. Gatica and A. Márquez, Analysis of a pseudostress-based mixed finite element method for the Brinkman model of porous media flow. Numer. Math. 126 (2014) 635–677. [CrossRef] [MathSciNet] [Google Scholar]
  30. J. Gopalakrishnan and M. Oh, Commuting smoothed projectors in weighted norms with an application to axisymmetric Maxwell equations. J. Sci. Comput. 51 (2012) 394–420. [CrossRef] [Google Scholar]
  31. J. Gopalakrishnan and J. Pasciak, The convergence of V-cycle multigrid algorithms for axisymmetric Laplace and Maxwell equations. Math. Comput. 75 (2006) 1697–1719. [CrossRef] [Google Scholar]
  32. R. Grauer and T.C. Sideris, Numerical computation of 3D incompressible ideal fluids with swirl. Phys. Rev. Lett. 67 (1991) 3511–3514. [CrossRef] [PubMed] [Google Scholar]
  33. A. Guardone and L. Vigevano, Finite element/volume solution to axisymmetric conservation laws. J. Comput. Phys. 224 (2007) 489–518. [CrossRef] [Google Scholar]
  34. J. Könnö and R. Stenberg, Numerical computations with H(div) −finite elements for the Brinkman problem. Comput. Geosci. 16 (2012) 139–158. [CrossRef] [Google Scholar]
  35. A. Kufner, Weighted Sobolev Spaces. Wiley, New York (1983). [Google Scholar]
  36. P. Lacoste, Solution of Maxwell equation in axisymmetric geometry by Fourier series decomposition and by use of H(rot) conforming finite element. Numer. Math. 84 (2000) 577–609. [CrossRef] [MathSciNet] [Google Scholar]
  37. Y.-J. Lee and H. Li, Axisymmetric Stokes equations in polygonal domains: Regularity and finite element approximations. Comput. Math. Appl. 64 (2012) 3500–3521. [CrossRef] [Google Scholar]
  38. Y.-J. Lee and H. Li, On stability, accuracy, and fast solvers for finite element approximations of the axisymmetric Stokes problem by Hood-Taylor elements. SIAM J. Numer. Anal. 49 (2011) 668–691. [CrossRef] [Google Scholar]
  39. J.-G. Liu and W.-C. Wang, Convergence analysis of the energy and helicity preserving scheme for axisymmetric flows. SIAM J. Numer. Anal. 44 (2006) 2456–2480. [CrossRef] [Google Scholar]
  40. K.A. Mardal, X.-C. Tai and R. Winther, A robust finite element method for Darcy–Stokes flow. SIAM J. Numer. Anal. 40 (2002) 1605–1631. [CrossRef] [MathSciNet] [Google Scholar]
  41. B. Mercier and G. Raugel, Resolution d’un problème aux limites dans un ouvert axisymétrique par éléments finis en r, z et séries de Fourier en θ. RAIRO Anal. Numér. 16 (1982) 405–461. [MathSciNet] [Google Scholar]
  42. G. Pontrelli, Blood flow through an axisymmetric stenosis. Proc. Int. Mech. Engrs. 215 (2001) H01–H10. [Google Scholar]
  43. K.R. Rajagopal, On a hierarchy of approximate models for flows of incompressible fluids through porous solids. Math. Models Methods Appl. Sci. 17 (2007) 215–252. [CrossRef] [MathSciNet] [Google Scholar]
  44. A. Riaz, M. Hesse and H.A. Tchelepi, Onset of convection in gravitationally unstable diffusive boundary layer in porous media. J. Fluid Mech. 548 (2006) 87–111. [CrossRef] [MathSciNet] [Google Scholar]
  45. V. Ruas, Mixed finite element methods with discontinuous pressures for the axisymmetric Stokes problem. ZAMM Z. Angew. Math. Mech. 83 (2003) 249–264. [CrossRef] [Google Scholar]
  46. C.G. Speziale, On the advantages of the vorticity-velocity formulations of the equations of fluid dynamics. J. Comput. Phys. 73 (1987) 476–480. [CrossRef] [Google Scholar]
  47. P.N. Tandon and U.V.S. Rana, A new model for blood flow through an artery with axisymmetric stenosis. Int. J. Biomed. Comput. 38 (1995) 257–267. [CrossRef] [PubMed] [Google Scholar]
  48. P. Vassilevski and U. Villa, A mixed formulation for the Brinkman problem. SIAM J. Numer. Anal. 52 (2014) 258–281. [CrossRef] [Google Scholar]

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