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.