A fractional-order trace-dev-div inequality
Abstract
The trace-dev-div inequality in Hs controls the trace in the norm of Hs by that of the deviatoric part plus the Hs-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 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 λ.
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