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arXiv · 2403.01291

A fractional-order trace-dev-div inequality

Carsten Carstensen·Norbert Heuer
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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 note. For mixed and least-squares finite element error analysis in linear elasticity, this inequality allows to establish robustness with respect to the Lamé parameter $λ$.

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Carsten Carstensen, Norbert Heuer. 2024-03-02. A fractional-order trace-dev-div inequality. https://arxiv.org/abs/2403.01291

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