A fractional-order trace-dev-div inequality
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913251692904448 |
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| author | Carstensen, Carsten Heuer, Norbert |
| author_facet | Carstensen, Carsten Heuer, Norbert |
| contents | 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 $λ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01291 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A fractional-order trace-dev-div inequality Carstensen, Carsten Heuer, Norbert Numerical Analysis Analysis of PDEs 35Q74, 35A23, 46E35, 35Q74, 74B05 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 $λ$. |
| title | A fractional-order trace-dev-div inequality |
| topic | Numerical Analysis Analysis of PDEs 35Q74, 35A23, 46E35, 35Q74, 74B05 |
| url | https://arxiv.org/abs/2403.01291 |