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

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−2d(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.