Optimal convergence rates in $L^2$ for a first order system least squares finite element method -- Part II: inhomogeneous Robin boundary conditions
<|reference_start|>Optimal convergence rates in $L^2$ for a first order system least squares finite element method -- Part II: inhomogeneous Robin boundary conditions: We consider divergence-based high order discretizations of an $L^2$-based first order system least squares formulation of a second order elliptic equation with Robin boundary conditions. For smooth geometries, we show optimal convergence rates in the $L^2(\Omega)$ norm for the scalar variable. Convergence rates for the $L^2(\Omega)$-norm error of the gradient of the scalar variable as well as vectorial variable are also derived. Numerical examples illustrate the analysis.<|reference_end|>
@article{bernkopf2024optimal,
    title={Optimal convergence rates in $L^2$ for a first order system least
  squares finite element method -- Part II: inhomogeneous Robin boundary
  conditions},
    author={Maximilian Bernkopf and Jens Markus Melenk},
    journal={arXiv preprint arXiv:2407.14424},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.14424},
    primaryClass={math.NA cs.NA}
}