OPTIMAL ERROR ESTIMATES FOR A SEMI-IMPLICIT EULER SCHEME FOR INCOMPRESSIBLE FLUIDS WITH SHEAR DEPENDENT VISCOSITIES.

Certain rheological behaviors of fluids in engineering sciences are modeled by power law ansatz with p ∈ (1, 2]. In the present paper a semi-implicit time discretization scheme for such fluids is proposed. The main result is the optimal O(k) error estimate, where k is the time step size. Our results hold in the range p ∈ (3/2, 2] (in the three-dimensional setting) for strong solutions of the continuous problem, whose existence is guaranteed under appropriate assumptions on the data. The estimates are uniform with respect to the degeneracy parameter δ ∈ [0, δ₀] of the extra stress tensor. Additional regularity properties of the solution of the discrete problem are proved. [ABSTRACT FROM AUTHOR]