by Carstensen, C. and Heuer, N.
Abstract:
Abstract 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 paper. For mixed and least-squares finite element error analysis in linear elasticity, this inequality allows to establish robustness with respect to the Lamé parameter $\lambda\$.
Reference:
Carstensen, C. and Heuer, N.: A fractional-order trace-dev-div inequality, Mathematische Nachrichten, volume 298, pp. 2493–2498, 2025.
Bibtex Entry:
@article{CH:FractionalorderTracedevdivInequality2025,
author = {Carstensen, C. and Heuer, N.},
title = {A fractional-order trace-dev-div inequality},
journal = {Mathematische Nachrichten},
volume = {298},
number = {8},
pages = {2493-2498},
keywords = {λ-robustness, fractional Sobolev spaces, Korn–Maxwell–Sobolev inequality, linear elasticity, regularity, trace-deviatoric-divergence inequality},
doi = {https://doi.org/10.1002/mana.70003},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/mana.70003},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/mana.70003},
abstract = {Abstract 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 paper. For mixed and least-squares finite element error analysis in linear elasticity, this inequality allows to establish robustness with respect to the Lamé parameter \$\lambda\$.},
year = {2025}
}