A fractional‐order trace‐dev‐div inequality

C. Carstensen and N. Heuer

Mathematische Nachrichten, 2025, vol. 298, issue 8, 2493-2498

Abstract: The trace‐dev‐div inequality in Hs$H^s$ controls the trace in the norm of Hs$H^s$ by that of the deviatoric part plus the Hs−1$H^{s-1}$ norm of the divergence of a quadratic tensor field different from the constant unit matrix. This is well known for s=0$s=0$ and established for orders 0≤s≤1$0\le s\le 1$ 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 λ$\lambda$.

Date: 2025
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