Convergence of a time discretization for a class of non-Newtonian fluid flow
Etienne Emmrich · Communications in Mathematical Sciences · 2008
The equation describing the non-stationary flow of an incompressible non-Newtonian fluid is approximated by the fully-and semi-implicit two-step backward differentiation formula (BDF).The stress tensor is assumed to be of p-structure such that the usual coercivity, growth, and monotonicity condition is fulfilled.Convergence of a piecewise polynomial prolongation of the discrete solution towards an exact weak solution is shown for the case p ≥ 1 + 2d/(d + 2), where d denotes the spatial dimension.