A fractional-order trace-dev-div inequality

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2025-07-13 DOI:10.1002/mana.70003

C. Carstensen, N. Heuer

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引用次数: 0

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 $0 \leq s \leq 1$ 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 $λ$ .

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分数阶trace-dev-div不等式

H s $H^s$中的迹迹-发展-分割不等式通过偏差部分的迹迹加上H s来控制H s $H^s$范数中的迹迹−1 $H^{s-1}$不同于常数单位矩阵的二次张量场的散度范数。这在s = 0 $s=0$时是已知的，在本文中对于阶数0≤s≤1 $0\le s\le 1$和任意空间维数都是成立的。对于线性弹性的混合和最小二乘有限元误差分析，该不等式允许建立关于lam参数λ $\lambda$的鲁棒性。

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index