Divergence conforming DG method for the optimal control of the Oseen equation with variable viscosity
<|reference_start|>Divergence conforming DG method for the optimal control of the Oseen equation with variable viscosity: This study introduces the divergence-conforming discontinuous Galerkin finite element method (DGFEM) for numerically approximating optimal control problems with distributed constraints, specifically those governed by stationary generalized Oseen equations. We provide optimal a priori error estimates in energy norms for such problems using the divergence-conforming DGFEM approach. Moreover, we thoroughly analyze $L^2$ error estimates for scenarios dominated by diffusion and convection. Additionally, we establish the new reliable and efficient a posteriori error estimators for the optimal control of the Oseen equation with variable viscosity. Theoretical findings are validated through numerical experiments conducted in both two and three dimensions.<|reference_end|>
@article{singh2024divergence,
    title={Divergence conforming DG method for the optimal control of the Oseen
  equation with variable viscosity},
    author={Harpal Singh and Arbaz Khan},
    journal={arXiv preprint arXiv:2403.15783},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.15783},
    primaryClass={math.NA cs.NA math.OC}
}