A stabilized finite element method on nonaffine grids for time-harmonic Maxwell's equations

被引：1
作者：
Du, Zhijie [1 ]
Duan, Huoyuan [2 ]
机构：
[1] Wuhan Univ Technol, Sch Nat Sci, Wuhan 430070, Peoples R China
[2] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China
来源：
BIT NUMERICAL MATHEMATICS | 2023年 / 63卷 / 04期
关键词：
Maxwell's equations; Finite element method; Grad-div stabilization; Uniform convergence; Edge element on nonaffine grid; ELECTROMAGNETIC-FIELDS; EDGE ELEMENTS; QUADRILATERALS; H(DIV); APPROXIMATION; SINGULARITIES; BOUNDARY;
D O I：
10.1007/s10543-023-00988-6
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
A stabilized mixed finite element method is proposed for solving the time-harmonic Maxwell's equations, with the divergence constraint imposed by the multiplier in a weak sense. By a grad-div stabilization, for some lowest-order edge elements on nonaffine quadrilateral, hexahedral and prismatic grids, we prove a type of uniform convergence for the zero-frequency Maxwell's equations, then prove the well-posedness and the convergence for the time-harmonic Maxwell's equations. Numerical results confirm the theoretical results.
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页数：32
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