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
收藏
页码：651 / 668
页数：18
相关论文
共 50 条
  • [31] A Quadratic C0 Interior Penalty Method for the Quad-Curl Problem
    Sun, Zhengjia
    Gao, Fuzheng
    Wang, Chao
    Zhang, Yi
    MATHEMATICAL MODELLING AND ANALYSIS, 2020, 25 (02) : 208 - 225
  • [32] A curl-conforming weak Galerkin method for the quad-curl problem
    Jiguang Sun
    Qian Zhang
    Zhimin Zhang
    BIT Numerical Mathematics, 2019, 59 : 1093 - 1114
  • [33] A curl-conforming weak Galerkin method for the quad-curl problem
    Sun, Jiguang
    Zhang, Qian
    Zhang, Zhimin
    BIT NUMERICAL MATHEMATICS, 2019, 59 (04) : 1093 - 1114
  • [34] BDDC DELUXE ALGORITHMS FOR TWO-DIMENSIONAL H(curl) ISOGEOMETRIC ANALYSIS
    Widlund, Olof B.
    Scacchid, Simone
    Pavarino, Luca F.
    SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2022, 44 (04): : A2349 - A2369
  • [35] Fast Method for Accelerating Time-Domain Solutions of Ill-Conditioned Electromagnetic Problems by Changing Curl-Curl Operator to Laplacian
    Xue, Li
    Jiao, Dan
    IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, 2021, 69 (11) : 4613 - 4622
  • [36] A DPG method for the quad-curl problem
    Fuhrer, Thomas
    Herrera, Pablo
    Heuer, Norbert
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2023, 149 : 221 - 238
  • [37] Multigrid methods for a quad-curl problem based on C0 interior penalty method
    Sun, Zhengjia
    Cui, Jintao
    Gao, Fuzheng
    Wang, Chao
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2018, 76 (09) : 2192 - 2211
  • [38] An hp-version interior penalty discontinuous Galerkin method for the quad-curl eigenvalue problem
    Han, Jiayu
    Zhang, Zhimin
    BIT NUMERICAL MATHEMATICS, 2023, 63 (04)
  • [39] An hp-version interior penalty discontinuous Galerkin method for the quad-curl eigenvalue problem
    Jiayu Han
    Zhimin Zhang
    BIT Numerical Mathematics, 2023, 63
  • [40] The interior penalty virtual element method for the two-dimensional biharmonic eigenvalue problem
    Meng, Jian
    Xu, Bing-Bing
    Su, Fang
    Qian, Xu
    COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2025, 436
12345