A fractional-order trace-dev-div inequality
<|reference_start|>A fractional-order trace-dev-div inequality: The trace-dev-div inequality in $H^s$ controls the trace in the norm of $H^s$ by that of the deviatoric part plus the $H^{s-1}$ norm of the divergence of a quadratic tensor field different from the constant unit matrix. This is well known for $s=0$ and established for orders $0\le s\le 1$ and arbitrary space dimension in this note. For mixed and least-squares finite element error analysis in linear elasticity, this inequality allows to establish robustness with respect to the Lam\'e parameter $\lambda$.<|reference_end|>
@article{carstensen2024a,
    title={A fractional-order trace-dev-div inequality},
    author={Carsten Carstensen and Norbert Heuer},
    journal={arXiv preprint arXiv:2403.01291},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.01291},
    primaryClass={math.NA cs.NA math.AP}
}