A Finite Element Method by Patch Reconstruction for the Quad-Curl Problem Using Mixed Formulations

被引:0
|
作者
Li, Ruo [1 ,2 ,3 ]
Liu, Qicheng [1 ]
Zhao, Shuhai [1 ]
机构
[1] Peking Univ, CAPT, LMAM, Beijing 100871, Peoples R China
[2] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
[3] Peking Univ, Chongqing Res Inst Big Data, Chongqing 401121, Peoples R China
基金
中国国家自然科学基金;
关键词
Quad-Curl problem; mixed formulation; patch reconstruction; DISCONTINUOUS GALERKIN METHOD; EQUATIONS;
D O I
10.4208/aamm.OA-2024-0086
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We develop a high order reconstructed discontinuous approximation (RDA) method for solving a mixed formulation of the quad-curl problem in two and three dimensions. This mixed formulation is established by adding an auxiliary variable to control the divergence of the field. The approximation space for the original variable is constructed by patch reconstruction with exactly one degree of freedom per element in each dimension and the auxiliary variable is approximated by the piecewise constant space. We prove the optimal convergence rate under the energy norm and also suboptimal L2 convergence using a duality approach. Numerical results are provided to verify the theoretical analysis.
引用
收藏
页码:517 / 537
页数:21
相关论文
共 50 条
  • [21] A Hybridizable Discontinuous Galerkin Method for the Quad-Curl Problem
    Gang Chen
    Jintao Cui
    Liwei Xu
    Journal of Scientific Computing, 2021, 87
  • [22] A Hybridizable Discontinuous Galerkin Method for the Quad-Curl Problem
    Chen, Gang
    Cui, Jintao
    Xu, Liwei
    JOURNAL OF SCIENTIFIC COMPUTING, 2021, 87 (01)
  • [23] Gradient recovery based finite element methods for the two-dimensional quad-curl problem
    Fang, Yuzhi
    Feng, Yuan
    Xu, Minqiang
    Zhang, Lei
    APPLIED MATHEMATICS LETTERS, 2023, 146
  • [24] Analysis of an interior penalty DG method for the quad-curl problem
    Chen, Gang
    Qiu, Weifeng
    Xu, Liwei
    IMA JOURNAL OF NUMERICAL ANALYSIS, 2021, 41 (04) : 2990 - 3023
  • [25] H(curl2)-Conforming Spectral Element Method for Quad-Curl Problems
    Wang, Lixiu
    Li, Huiyuan
    Zhang, Zhimin
    COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, 2021, 21 (03) : 661 - 681
  • [26] H(curl2)-conforming quadrilateral spectral element method for quad-curl problems
    Wang, Lixiu
    Shan, Weikun
    Li, Huiyuan
    Zhang, Zhimin
    MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2021, 31 (10): : 1951 - 1986
  • [27] H(curl2)-conforming triangular spectral element method for quad-curl problems
    Wang, Lixiu
    Li, Huiyuan
    Zhang, Qian
    Zhang, Zhimin
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2025, 459
  • [28] H(CURL2)-CONFORMING FINITE ELEMENTS IN 2 DIMENSIONS AND APPLICATIONS TO THE QUAD-CURL PROBLEM
    Zhang, Qian
    Wang, Lixiu
    Zhang, Zhimin
    SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2019, 41 (03): : A1527 - A1547
  • [29] 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
  • [30] A priori and a posteriori error estimates for the quad-curl eigenvalue problem
    Wang, Lixiu
    Zhang, Qian
    Sun, Jiguang
    Zhang, Zhimin
    ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS, 2022, 56 (03) : 1027 - 1051