Optimal error estimate for a space-time discretization for incompressible generalized Newtonian fluids: The Dirichlet problem

Luigi C. Berselli, Michael Růžička

In this paper we prove optimal error estimates for {solutions with natural regularity} of the equations describing the unsteady motion of incompressible shear-thinning fluids. We consider a full space-time semi-implicit scheme for the discretization. The main novelty, with respect to previous results, is that we obtain the estimates directly without introducing intermediate semi-discrete problems, which enables the treatment of homogeneous Dirichlet boundary conditions.

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