Publication Cover
Applicable Analysis
An International Journal
Volume 95, 2016 - Issue 2
114
Views
0
CrossRef citations to date
0
Altmetric
Articles

A stabilized finite element analysis for a power-law pseudoplastic Stokes problem

&
Pages 467-482 | Received 06 Aug 2014, Accepted 15 Jan 2015, Published online: 09 Feb 2015

References

  • Brezzi F. On the existence, uniqueness and approximation of saddle-point problems arising from lagrange multipliers. M2AN ESAIM: Math. Model. Numer. Anal. 1974;8:129–151.
  • Babuska I. Error bounds for finite element method. Numer. Math. 1971;16:322–333.
  • Babuska I. The finite element method with penalty. Math. Comput. 1973;27:221–228.
  • Borggaard J, Iliescu T, Roop JP. An improved penalty method for Power-Law Stokes problem. J. Comput. Appl. Math. 2009;223:646–658.
  • Congreve S, Houston P, Suli E, Wihler TP. Discontinuous galerkin finite element approximation of quasilinear elliptic boundary value problems ii: strongly monotone quasi-newtonian flows. IMA J. Numer. Anal. 2013;33:1386–1415.
  • Lefton L, Wei D. A penalty method for approximate of the stationary Power-Law Stokes problem. Eletron. J. Differ. Equ. 2000;2000:1–13.
  • Karam-Filho J. Loula AFD. A non-standard application of Babuska-Brezzi theory to finite element analysis of Stokes problem. Comput. Appl. Math. 1991;10:243–262.
  • Karam Filho J, Loula AFD. On stable equal-order finite element formulations for incompressible flow problems. Int. J. Numer. Method. Eng. 1992;34:655–665.
  • Loula AF, Guerreiro JN. Finite element analysis of nonlinear creeping flows. Comput. Meth. Appl. Mech. Eng. 1990;79:87–109.
  • Becker R, Braack M. A finite element pressure gradient stabilization for the Stokes equations based on local projections. Calcolo. 2001;38:173–199.
  • Belenki L, Berselli LC, Diening L, R\r{u}\v{z}i\v{c}ka M. On the finite element approximation of p-Stokes systems. SIAM J. Numer. Anal. 2012;50:373–397.
  • Bochev PB, Dohrmann CR, Gunzburger MD. Stabilization of low-order mixed finite elements for the Stokes equations. SIAM J. Numer. Anal. 2006;44:82–101.
  • Hirn A. Approximation of the p-Stokes equations with equal-order finite elements. J. Math. Fluid Mech. 2013;15:65–88.
  • Xie C, Feng M. A new stabilized method for quasi-Newtonian flows. Appl. Math. Mech. 2010;31:1081–1096. English.
  • Baranger J, Najib K, Sandri D. Numerical analysis of a three-fields model for a quasi-newtonian flow. Comput. Meth. Appl. Mech. Eng. 1993;109:281–292.
  • Ervin VJ, Phillips TN. Residual a posteriori error estimator for a three-field model of a non-linear generalized Stokes problem. Comput. Meth. Appl. Mech. Eng. 2006;195:2599–2610.
  • Gatica GN, Márquez A, Sánchez MA. A priori and a posteriori error analyses of a velocity-pseudostress formulation for a class of quasi-newtonian Stokes flow. Comput. Meth. Appl. Mech. Eng. 2001;200:1619–1637.
  • Manouzi H, Farhloul M. Mixed finite element analysis of a non-linear three-fields Stokes model. IMA J. Numer. Anal. 2001;21:143–164.
  • Bustinza R, Gatica GN. A mixed local discontinuous galerkin method for a class of nonlinear problems in fluid mechanics. J. Comput. Phys. 2005;207:427–456.
  • Scheurer B. Existence et approximation de points selles pour certains problèmes non linéaires [Existence and approximation of saddle points for some nonlinear problems]. RAIRO Anal. Numer. 1997;11:369–400.
  • Bird RB, Armstrong RC, Hassager O. Dynamics of polymeric liquids. 2nd ed. Vol. 1. New York (NY): Wiley; 1987.
  • Lions JL. Quelques méthods de résolution des problèmes aux limites non linéaires [Some resolution methods for nonlinear boundary value prolems]. Paris: Dunod; 1969.
  • Růžička M. A note on steady flow of fluids with shear dependent viscosity. Nonlinear Anal. Theory Meth. Appl. 1997;30:3029–3039.
  • Adams RA. Sobolev spaces. Pure and applied mathematics series. New York (NY): Academic Press; 1975.
  • Brenner SC, Scott LR. The mathematical theory of finite element methods. 3rd ed. New York (NY): Springer; 2008.
  • Fortin M. Old and new finite elements for incompressible flows. Int. J. Numer. Meth. Fluids. 1981;1:347–431.
  • Hughes JR. The finite element method: Linear static and dynamic finite element analysis. New York (NY): Dover; 2000.
  • Ciarlet PG. The finite element method for elliptic problems. Amsterdam: North-Holland; 1978.
  • Glowinski R, Marroco A. Sur lapproximation, par éléments finis dordre un, et la résolution, par pénalisation-dualité dune classe de problémes de dirichlet non linéaires [On the first-order finite element approximation and the penalization-duality solution for a class of nonlinear Dirichlet problem]. RAIRO Anal. Numer. 1975;9:41–76.
  • Harari I, Hughes TJR. What are C and h? Inequalities for the analysis and design of finite element method. Comput. Meth. Appl. Mech. Eng. 1992;97:157–192.
  • Carey GF, Oden JT. Finite elements: a second course. The Texas finite element series. Englewood Cliffs (NJ): Prentice-Hall; 1983.
  • Soulaimani A, Fortin M, Ouellet Y, Dhatt G, Bertrand F. Simple continuous pressure elements for two- and three- dimensional incompressible flows. Comput. Meth. Appl. Mech. Eng. 1987;62:47–69.
  • Lee RL, Gresho PM, Sani RL. Smoothing techniques for certain primitive variable solutions of the Navier-Stokes equations. Int. J. Numer. Meth. Eng. 1979;14:1785–1804.
  • Franca LP, Karam-Filho J, Loula AFD, Stemberg R. A convergence analysis of a stabilized method for the Stokes flow. Comput. Appl. Math. 1991;10:19–26.
  • Skrzypek JJ. Plasticity and creep: theory, examples and problems. Boca Raton (FL): Begel House; 1993.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.