Convergence analysis for a finite element approximation of a steady model for electrorheological fluids

Berselli LC, Breit D, Diening L. Convergence analysis for a finite element approximation of a steady model for electrorheological fluids. Numerische Mathematik. 2016;132(4):657-689.In this paper we study the finite element approximation of systems of $p(\cdot)$-Stokes type, where $p(\cdot)$ is a (non constant) given function of the space variables. We derive --in some cases optimal-- error estimates for finite element approximation of the velocity and of the pressure, in a suitable functional setting