A NONCONFORMING FINITE ELEMENT METHOD FOR FOURTH ORDER CURL EQUATIONS IN R3

被引：55
|
作者：
Zheng, Bin [1 ]
Hu, Qiya [2 ]
Xu, Jinchao [1 ]
机构：
[1] Penn State Univ, Dept Math, Ctr Computat Math & Applicat, University Pk, PA 16802 USA
[2] Chinese Acad Sci, LSEC, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100080, Peoples R China
来源：
MATHEMATICS OF COMPUTATION | 2011年 / 80卷 / 276期
基金：
美国国家科学基金会;
关键词：
MAGNETOHYDRODYNAMIC EQUATIONS; MAGNETO-HYDRODYNAMICS; APPROXIMATION; ORDER;
D O I：
10.1090/S0025-5718-2011-02480-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we present a nonconforming finite element method for solving fourth order curl equations in three dimensions arising from magnetohydrodynamics models. We show that the method has an optimal error estimate for a model problem involving both (del x)(2) and (del x)(4) operators. The element has a very small number of degrees of freedom, and it imposes the inter-element continuity along the tangential direction which is appropriate for the approximation of magnetic fields. We also provide explicit formulae of basis functions for this element.
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页码：1871 / 1886
页数：16
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