A stabilized finite element method to pseudoplastic flow governed by the Sisko relation

in this work, a consistent stabilized mixed finite element formulation for incompressible pseudoplastic fluid flows governed by the sisko constitutive equation is mathematically analysed. this formulation is constructed by adding least-squares of the governing equations and of the incompressibility constraint, with discontinuous pressure approximations, allowing the use of same order interpolations for the velocity and the pressure. numerical results are presented to confirm the mathematical stability analysis. mathematical subject classification: primary: 65m60; secondary: 65n30.