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.
引用
收藏
页数：32
相关论文
共 50 条
  • [41] Time Domain Finite Element Method for Maxwell's Equations
    Anees, Asad
    Angermann, Lutz
    IEEE ACCESS, 2019, 7 : 63852 - 63867
  • [42] On the solution of time-harmonic scattering problems for Maxwell's equations
    Hazard, C
    Lenoir, M
    SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1996, 27 (06) : 1597 - 1630
  • [43] A Preconditioned Dual-Primal Finite Element Tearing and Interconnecting Method for Solving 3D Time-Harmonic Maxwell's Equations
    Xue, M. F.
    Jin, J. M.
    2014 INTERNATIONAL CONFERENCE ON ELECTROMAGNETICS IN ADVANCED APPLICATIONS (ICEAA), 2014, : 18 - 21
  • [44] A preconditioned dual-primal finite element tearing and interconnecting method for solving three-dimensional time-harmonic Maxwell's equations
    Xue, Ming-Feng
    Jin, Jian-Ming
    JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 274 : 920 - 935
  • [45] Nonlinear time-harmonic Maxwell equations in domains
    Thomas Bartsch
    Jarosław Mederski
    Journal of Fixed Point Theory and Applications, 2017, 19 : 959 - 986
  • [46] Nonlinear time-harmonic Maxwell equations in domains
    Bartsch, Thomas
    Mederski, Jarosaw
    JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2017, 19 (01) : 959 - 986
  • [47] Discrete boundary finite element schemes for an exterior problem for the time-harmonic Maxwell's equation
    Maatouk, Khalil
    APPLIED MATHEMATICS AND COMPUTATION, 2014, 242 : 361 - 387
  • [48] Schwarz Preconditioning for High Order Edge Element Discretizations of the Time-Harmonic Maxwell's Equations
    Bonazzoli, Marcella
    Dolean, Victorita
    Pasquetti, Richard
    Rapetti, Francesca
    DOMAIN DECOMPOSITION METHODS IN SCIENCE AND ENGINEERING XXIII, 2017, 116 : 117 - 124
  • [49] Fast Evaluation of Time-Harmonic Maxwell's Equations Using the Reduced Basis Method
    Hess, Martin W.
    Benner, Peter
    IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, 2013, 61 (06) : 2265 - 2274
  • [50] A VARIANT OF THE PLANE WAVE LEAST SQUARES METHOD FOR THE TIME-HARMONIC MAXWELL'S EQUATIONS
    Hu, Qiya
    Song, Rongrong
    ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2019, 53 (01): : 85 - 103
12345