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

TL;DR

This paper establishes optimal error estimates for a space-time discretization scheme applied to incompressible shear-thinning fluids, directly handling boundary conditions without intermediate problems, advancing numerical analysis in fluid dynamics.

Contribution

It provides the first direct error estimates for the full space-time scheme for shear-thinning fluids with homogeneous Dirichlet boundary conditions.

Findings

Achieved optimal error bounds for the discretization scheme.

Extended analysis to handle boundary conditions directly.

Improved understanding of numerical methods for non-Newtonian fluids.

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.