A nonconforming finite element method for a two-dimensional curl-curl and grad-div problem

被引：39
作者：
Brenner, S. C. [1 ,2 ]
Cui, J. [1 ]
Li, F. [3 ]
Sung, L. -Y. [1 ]
机构：
[1] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA
[2] Louisiana State Univ, Ctr Computat & Technol, Baton Rouge, LA 70803 USA
[3] Rensselaer Polytech Inst, Dept Math Sci, Troy, NY 12180 USA
来源：
NUMERISCHE MATHEMATIK | 2008年 / 109卷 / 04期
基金：
美国国家科学基金会;
关键词：
curl-curl and grad-div problem; nonconforming finite element methods; Maxwell equations;
D O I：
10.1007/s00211-008-0149-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A numerical method for a two-dimensional curl-curl and grad-div problem is studied in this paper. It is based on a discretization using weakly continuous P-1 vector fields and includes two consistency terms involving the jumps of the vector fields across element boundaries. Optimal convergence rates ( up to an arbitrary positive is an element of) in both the energy norm and the L-2 norm are established on graded meshes. The theoretical results are confirmed by numerical experiments.
引用
收藏
页码：509 / 533
页数：25
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