H(CURL2)-CONFORMING FINITE ELEMENTS IN 2 DIMENSIONS AND APPLICATIONS TO THE QUAD-CURL PROBLEM

被引：38

作者：

Zhang, Qian ^{[1
]}

Wang, Lixiu ^{[1
]}

Zhang, Zhimin ^{[1
,2
]}

机构：

[1] Beijing Computat Sci Res Ctr, Beijing 100193, Peoples R China

[2] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2019年 / 41卷 / 03期

基金：

美国国家科学基金会; 中国国家自然科学基金;

关键词：

H(curl(2))-conforming finite elements; DISCONTINUOUS GALERKIN METHOD; SUPERCONVERGENCE ANALYSIS; MAXWELLS EQUATIONS; CONVERGENCE; MESHES;

D O I：

10.1137/18M1199988

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we construct some H(curl(2))-conforming finite elements on a rectangle (a parallelogram) and a triangle. The proposed elements possess some nice properties which have been proved by a rigorous theoretical analysis. Then we apply our new elements to construct a finite element space for discretizing the quad-curl problem. Convergence orders O(h(k)) in the H(curl) norm and O(h(k-1)) in the H(curl(2)) norm are established. Numerical experiments are provided to confirm the theoretical results.

引用

页码：A1527 / A1547

页数：21

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