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
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