多边形和多面体网格上的宏 BDM H-div 混合有限元

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2024-08-22 DOI:10.1016/j.apnum.2024.08.013

Xuejun Xu , Xiu Ye , Shangyou Zhang

{"title":"多边形和多面体网格上的宏 BDM H-div 混合有限元","authors":"Xuejun Xu , Xiu Ye , Shangyou Zhang","doi":"10.1016/j.apnum.2024.08.013","DOIUrl":null,"url":null,"abstract":"<div>A BDM type of <math><mi>H</mi><mo>(</mo><mi>div</mi><mo>)</mo></math> mixed finite element is constructed on polygonal and polyhedral meshes. The flux space is the <math><mi>H</mi><mo>(</mo><mi>div</mi><mo>)</mo></math> subspace of the n-product <math><msub><mrow><mi>Π</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi></mrow></msub><msup><mrow><mo>(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>d</mi></mrow></msup></math> space such that the divergence is a one-piece <math><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub></math> polynomial on the big polygon or polyhedron T. Here we assume the 2D polygon can be subdivided into triangles by connecting only one vertex with some vertices of the polygon. For the 3D polyhedron we assume it can be subdivided into tetrahedra, with no added vertex on subdividing its face-polygons, and with either no internal edge or one internal edge. Such mixed finite elements can be more economic on quadrilateral and hexahedral meshes, compared with the standard BDM mixed element on triangular and tetrahedral meshes. Numerical tests and comparisons with the triangular and tetrahedral BDM finite elements are provided.</div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"206 ","pages":"Pages 283-297"},"PeriodicalIF":2.2000,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A macro BDM H-div mixed finite element on polygonal and polyhedral meshes\",\"authors\":\"Xuejun Xu , Xiu Ye , Shangyou Zhang\",\"doi\":\"10.1016/j.apnum.2024.08.013\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>A BDM type of <math><mi>H</mi><mo>(</mo><mi>div</mi><mo>)</mo></math> mixed finite element is constructed on polygonal and polyhedral meshes. The flux space is the <math><mi>H</mi><mo>(</mo><mi>div</mi><mo>)</mo></math> subspace of the n-product <math><msub><mrow><mi>Π</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi></mrow></msub><msup><mrow><mo>(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>d</mi></mrow></msup></math> space such that the divergence is a one-piece <math><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub></math> polynomial on the big polygon or polyhedron T. Here we assume the 2D polygon can be subdivided into triangles by connecting only one vertex with some vertices of the polygon. For the 3D polyhedron we assume it can be subdivided into tetrahedra, with no added vertex on subdividing its face-polygons, and with either no internal edge or one internal edge. Such mixed finite elements can be more economic on quadrilateral and hexahedral meshes, compared with the standard BDM mixed element on triangular and tetrahedral meshes. Numerical tests and comparisons with the triangular and tetrahedral BDM finite elements are provided.</div>\",\"PeriodicalId\":8199,\"journal\":{\"name\":\"Applied Numerical Mathematics\",\"volume\":\"206 \",\"pages\":\"Pages 283-297\"},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-08-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Numerical Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0168927424002095\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Numerical Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0168927424002095","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

摘要

在多边形和多面体网格上构建了 BDM 类型的 H(div) 混合有限元。通量空间是 n 积 ΠiPk(Ti)d 空间的 H(div) 子空间，其发散是大多边形或多面体 T 上的一次 Pk-1 多项式。对于三维多面体，我们假设它可以细分为四面体，在细分其面多面体时不增加顶点，并且没有内边或只有一条内边。与三角形和四面体网格上的标准 BDM 混合元素相比，这种混合有限元在四边形和六面体网格上更经济。本文提供了数值测试以及与三角形和四面体 BDM 有限元的比较。

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 macro BDM H-div mixed finite element on polygonal and polyhedral meshes

A BDM type of $H (div)$ mixed finite element is constructed on polygonal and polyhedral meshes. The flux space is the $H (div)$ subspace of the n-product $Π_{i} P_{k} {(T_{i})}^{d}$ space such that the divergence is a one-piece $P_{k - 1}$ polynomial on the big polygon or polyhedron T. Here we assume the 2D polygon can be subdivided into triangles by connecting only one vertex with some vertices of the polygon. For the 3D polyhedron we assume it can be subdivided into tetrahedra, with no added vertex on subdividing its face-polygons, and with either no internal edge or one internal edge. Such mixed finite elements can be more economic on quadrilateral and hexahedral meshes, compared with the standard BDM mixed element on triangular and tetrahedral meshes. Numerical tests and comparisons with the triangular and tetrahedral BDM finite elements are provided.

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

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.