Optimal error estimate for a space-time discretization for incompressible generalized Newtonian fluids: the Dirichlet problem
Luigi C. Berselli, Michael Růžička · Partial Differential Equations and Applications · 2021
Abstract 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.