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In this paper, we examine a finite element approximation of the steady$p(\cdot)$-Navier-Stokes equations ($p(\cdot)$ is variable dependent) and proveorders of convergence by assuming natural fractional regularity assumptions onthe velocity vector field and the kinematic pressure. Compared to previousresults, we treat the convective term and employ a more practicablediscretization of the power-law index $p(\cdot)$. Numerical experiments confirmthe quasi-optimality of the a priori error estimates (for the velocity) withrespect to fractional regularity assumptions on the velocity vector field andthe kinematic pressure.

Error analysis for a finite element approximation of the steady $p(\cdot)$-Navier-Stokes equations