A new div-div-conforming symmetric tensor finite element space with applications to the biharmonic equation

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Mathematics of Computation Pub Date : 2024-02-22 DOI:10.1090/mcom/3957

Long Chen, Xuehai Huang

{"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":18456,"journal":{"name":"Mathematics of Computation","volume":"38 1","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of Computation","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/mcom/3957","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

A new H ( div ⁡ div ) 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 C 0 C^0 discontinuous Galerkin methods for the biharmonic equation are derived.

查看原文本刊更多论文

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

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Mathematics of Computation 数学-应用数学

CiteScore

3.90

自引率

5.00%

发文量

审稿时长

7.0 months

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in computational mathematics. Areas covered include numerical analysis, computational discrete mathematics, including number theory, algebra and combinatorics, and related fields such as stochastic numerical methods. Articles must be of significant computational interest and contain original and substantial mathematical analysis or development of computational methodology.