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 ≤ s≤ 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.