Finite element discretization of the steady, generalized Navier-Stokes equations for small shear stress exponents
<|reference_start|>Finite element discretization of the steady, generalized Navier-Stokes equations for small shear stress exponents: A finite element (FE) discretization for the steady, incompressible, fully inhomogeneous, generalized Navier-Stokes equations is proposed. By the method of divergence reconstruction operators, the formulation is valid for all shear stress exponents $p > \tfrac{2d}{d+2}$. The Dirichlet boundary condition is imposed strongly, using any discretization of the boundary data which converges at a sufficient rate. $\textit{A priori}$ error estimates for velocity vector field and kinematic pressure are derived and numerical experiments are conducted. These confirm the quasi-optimality of the $\textit{a priori}$ error estimate for the velocity vector field. The $\textit{a priori}$ error estimates for the kinematic pressure are quasi-optimal if $p \leq 2$.<|reference_end|>
@article{kaltenbach2024finite,
    title={Finite element discretization of the steady, generalized Navier-Stokes
  equations for small shear stress exponents},
    author={Alex Kaltenbach and Julius Je{ss}berger},
    journal={arXiv preprint arXiv:2408.15731},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.15731},
    primaryClass={math.NA cs.NA}
}