A posteriori estimators for mixed finite element approximations of a fluid obeying the power law

We study a posteriori error estimation in the approximation by the finite element method of a fluid which obeys the power law: −2μ▽·(¦ d( u)¦ r−2 d( u)) + ▽p = f, ▽.u = 0, 1 < r < 2. Abstract and calculable a posteriori estimators are given in two-fields and in a three-fields version of this problem. Furthermore, we give some examples of FE spaces satisfying the inf-sup condition, which relates the discrete space of tensors and the discrete space of velocities, needed for this formulation.