分数阶trace-dev-div不等式

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

{"title":"分数阶trace-dev-div不等式","authors":"C. Carstensen, N. Heuer","doi":"10.1002/mana.70003","DOIUrl":null,"url":null,"abstract":"The trace-dev-div inequality in <math>\n <semantics>\n <msup>\n <mi>H</mi>\n <mi>s</mi>\n </msup>\n <annotation>$H^s$</annotation>\n </semantics></math> controls the trace in the norm of <math>\n <semantics>\n <msup>\n <mi>H</mi>\n <mi>s</mi>\n </msup>\n <annotation>$H^s$</annotation>\n </semantics></math> by that of the deviatoric part plus the <math>\n <semantics>\n <msup>\n <mi>H</mi>\n <mrow>\n <mi>s</mi>\n <mo>−</mo>\n <mn>1</mn>\n </mrow>\n </msup>\n <annotation>$H^{s-1}$</annotation>\n </semantics></math> norm of the divergence of a quadratic tensor field different from the constant unit matrix. This is well known for <math>\n <semantics>\n <mrow>\n <mi>s</mi>\n <mo>=</mo>\n <mn>0</mn>\n </mrow>\n <annotation>$s=0$</annotation>\n </semantics></math> and established for orders <math>\n <semantics>\n <mrow>\n <mn>0</mn>\n <mo>≤</mo>\n <mi>s</mi>\n <mo>≤</mo>\n <mn>1</mn>\n </mrow>\n <annotation>$0\\le s\\le 1$</annotation>\n </semantics></math> 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 <math>\n <semantics>\n <mi>λ</mi>\n <annotation>$\\lambda$</annotation>\n </semantics></math>.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 8","pages":"2493-2498"},"PeriodicalIF":0.8000,"publicationDate":"2025-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70003","citationCount":"0","resultStr":"{\"title\":\"A fractional-order trace-dev-div inequality\",\"authors\":\"C. Carstensen, N. Heuer\",\"doi\":\"10.1002/mana.70003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The trace-dev-div inequality in <math>\\n <semantics>\\n <msup>\\n <mi>H</mi>\\n <mi>s</mi>\\n </msup>\\n <annotation>$H^s$</annotation>\\n </semantics></math> controls the trace in the norm of <math>\\n <semantics>\\n <msup>\\n <mi>H</mi>\\n <mi>s</mi>\\n </msup>\\n <annotation>$H^s$</annotation>\\n </semantics></math> by that of the deviatoric part plus the <math>\\n <semantics>\\n <msup>\\n <mi>H</mi>\\n <mrow>\\n <mi>s</mi>\\n <mo>−</mo>\\n <mn>1</mn>\\n </mrow>\\n </msup>\\n <annotation>$H^{s-1}$</annotation>\\n </semantics></math> norm of the divergence of a quadratic tensor field different from the constant unit matrix. This is well known for <math>\\n <semantics>\\n <mrow>\\n <mi>s</mi>\\n <mo>=</mo>\\n <mn>0</mn>\\n </mrow>\\n <annotation>$s=0$</annotation>\\n </semantics></math> and established for orders <math>\\n <semantics>\\n <mrow>\\n <mn>0</mn>\\n <mo>≤</mo>\\n <mi>s</mi>\\n <mo>≤</mo>\\n <mn>1</mn>\\n </mrow>\\n <annotation>$0\\\\le s\\\\le 1$</annotation>\\n </semantics></math> 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 <math>\\n <semantics>\\n <mi>λ</mi>\\n <annotation>$\\\\lambda$</annotation>\\n </semantics></math>.\",\"PeriodicalId\":49853,\"journal\":{\"name\":\"Mathematische Nachrichten\",\"volume\":\"298 8\",\"pages\":\"2493-2498\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2025-07-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70003\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematische Nachrichten\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mana.70003\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematische Nachrichten","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mana.70003","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

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 $0 \leq s \leq 1$ 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 $λ$ .

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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