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

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS

ACS Applied Bio Materials Pub Date : 2024-08-22 DOI:10.1016/j.apnum.2024.08.013

Xuejun Xu , Xiu Ye , Shangyou Zhang

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引用次数: 0

Abstract

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.

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多边形和多面体网格上的宏 BDM H-div 混合有限元

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。

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来源期刊

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464