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

被引：57

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.

引用

页码：1871 / 1886

页数：16