Convergence analysis for a fully-discrete finite element approximation of the unsteady $p(\cdot,\cdot)$-Navier-Stokes equations
<|reference_start|>Convergence analysis for a fully-discrete finite element approximation of the unsteady $p(\cdot,\cdot)$-Navier-Stokes equations: In the present paper, we establish the well-posedness, stability, and (weak) convergence of a fully-discrete approximation of the unsteady $p(\cdot,\cdot)$-Navier-Stokes equations employing an implicit Euler step in time and a discretely inf-sup-stable finite element approximation in space. Moreover, numerical experiments are carried out that supplement the theoretical findings.<|reference_end|>
@article{berselli2024convergence,
    title={Convergence analysis for a fully-discrete finite element approximation
  of the unsteady $p(\cdot,\cdot)$-Navier-Stokes equations},
    author={Luigi C. Berselli and Alex Kaltenbach},
    journal={arXiv preprint arXiv:2402.16606},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.16606},
    primaryClass={math.NA cs.NA}
}