A NONCONFORMING PENALTY METHOD FOR A TWO-DIMENSIONAL CURL-CURL PROBLEM

被引：9

作者：

Brenner, Susanne C. ^{[1
,2
]}

Li, Fengyan ^{[3
]}

Sung, Li-Yeng ^{[2
]}

机构：

[1] Louisiana State Univ, Ctr Computat & Technol, Baton Rouge, LA 70803 USA

[2] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA

[3] Rensselaer Polytech Inst, Dept Math Sci, Troy, NY 12180 USA

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2009年 / 19卷 / 04期

基金：

美国国家科学基金会;

关键词：

Curl-curl problem; Maxwell equations; Maxwell eigenvalues; nonconforming finite element method; DISCONTINUOUS GALERKIN APPROXIMATION; HARMONIC MAXWELL EQUATIONS; MIXED FINITE-ELEMENTS; WEIGHTED REGULARIZATION; POLYHEDRAL DOMAINS; OPERATOR; CONVERGENCE;

D O I：

10.1142/S0218202509003565

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A nonconforming finite element method for a two-dimensional curl-curl problem is studied in this paper. It uses weakly continuous P(1) vector fields and penalizes the local divergence. Two consistency terms involving the jumps of the vector fields across element boundaries are also included to ensure the convergence of the scheme. Optimal convergence rates ( up to an arbitrary positive epsilon) in both the energy norm and the L(2) norm are established on graded meshes. This scheme can also be used in the computation of Maxwell eigenvalues without generating spurious eigenmodes. The theoretical results are confirmed by numerical experiments.

引用

页码：651 / 668

页数：18

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