STABLE AND COMPATIBLE POLYNOMIAL EXTENSIONS IN THREE DIMENSIONS AND APPLICATIONS TO THE p AND h-p FINITE ELEMENT METHOD

被引：16

作者：

Guo, Benqi ^{[1
,2
]}

Zhang, Jianming ^{[2
]}

机构：

[1] Shanghai Normal Univ, Dept Math, Shanghai, Peoples R China

[2] Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2009年 / 47卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

the p and h-p version; finite elememt method; polynomial extension; tetrahedron; hexahedron; prism; pyramid; cube; Sobolev spaces; Jacobi polynomials; INVERSE APPROXIMATION THEOREMS; WEIGHTED BESOV-SPACES; OPTIMAL CONVERGENCE; VERSION; FRAMEWORK;

D O I：

10.1137/070688006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Polynomial extensions play a vital role in the analysis of the p and h-p finite element method (FEM) and the spectral element method. We construct explicitly polynomial extensions on standard elements: cubes and triangular prisms, which together with the extension on tetrahedrons are used by the p and h-p FEM in three dimensions. These extensions are proved to be stable and compatible with FEM subspaces on tetrahedrons, cubes, and prisms and realize a continuous mapping: H-00(1/2)(T) (or H-00(1/2) (S)) -> H-1(Omega(st)), where Omega(st) denotes one of these standard elements and T and S are their triangular and square faces. Applications of these polynomial extensions to the p and h-p FEM are illustrated.

引用

页码：1195 / 1225

页数：31

共 29 条

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[2] The Convergence of the h-p Version of the Finite Element Method with Quasi-uniform Meshes in Three Dimensions
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[4] Construction of polynomial extensions in two dimensions and application to the h-p finite element method Reprinted of Journal of Computational and Applied Mathematics, vol 261, pg 249-270, 2014)
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