{"title":"一种新的二分对称张量有限元空间及其在双谐波方程中的应用","authors":"Long Chen, Xuehai Huang","doi":"10.1090/mcom/3957","DOIUrl":null,"url":null,"abstract":"<p>A new <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H left-parenthesis d i v d i v right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>div</mml:mi> <mml:mo><!-- --></mml:mo> <mml:mi>div</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">H(\\operatorname {div}\\operatorname {div})</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-conforming finite element is presented, which avoids the need for supersmoothness by redistributing the degrees of freedom to edges and faces. This leads to a hybridizable mixed method with superconvergence for the biharmonic equation. Moreover, new finite element divdiv complexes are established. Finally, new weak Galerkin and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Superscript 0\"> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">C^0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> discontinuous Galerkin methods for the biharmonic equation are derived.</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A new div-div-conforming symmetric tensor finite element space with applications to the biharmonic equation\",\"authors\":\"Long Chen, Xuehai Huang\",\"doi\":\"10.1090/mcom/3957\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>A new <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper H left-parenthesis d i v d i v right-parenthesis\\\"> <mml:semantics> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo stretchy=\\\"false\\\">(</mml:mo> <mml:mi>div</mml:mi> <mml:mo><!-- --></mml:mo> <mml:mi>div</mml:mi> <mml:mo stretchy=\\\"false\\\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\\\"application/x-tex\\\">H(\\\\operatorname {div}\\\\operatorname {div})</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-conforming finite element is presented, which avoids the need for supersmoothness by redistributing the degrees of freedom to edges and faces. This leads to a hybridizable mixed method with superconvergence for the biharmonic equation. Moreover, new finite element divdiv complexes are established. Finally, new weak Galerkin and <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper C Superscript 0\\\"> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:annotation encoding=\\\"application/x-tex\\\">C^0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> discontinuous Galerkin methods for the biharmonic equation are derived.</p>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-02-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/mcom/3957\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/mcom/3957","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
摘要
本文提出了一种新的 H ( div div ) H(\operatorname {div}\operatorname {div}) 顺应有限元，通过将自由度重新分配到边和面，避免了对超平滑性的需求。这就为双谐波方程带来了一种具有超收敛性的可混合混合方法。此外，还建立了新的有限元 divdiv 复数。最后，推导出了双谐波方程的新弱 Galerkin 方法和 C 0 C^0 非连续 Galerkin 方法。
A new div-div-conforming symmetric tensor finite element space with applications to the biharmonic equation
A new H(divdiv)H(\operatorname {div}\operatorname {div})-conforming finite element is presented, which avoids the need for supersmoothness by redistributing the degrees of freedom to edges and faces. This leads to a hybridizable mixed method with superconvergence for the biharmonic equation. Moreover, new finite element divdiv complexes are established. Finally, new weak Galerkin and C0C^0 discontinuous Galerkin methods for the biharmonic equation are derived.
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