Fully discrete A -ϕ finite element method for Maxwell's equations with nonlinear conductivity

2014 ◽  
Vol 30 (6) ◽  
pp. 2083-2108 ◽  
Author(s):  
Tong Kang ◽  
Tao Chen ◽  
Huai Zhang ◽  
Kwang Ik Kim
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Nonlinear Conductivity ◽  
Fully Discrete ◽  
Element Method

Fully Discrete A-ø Finite Element Method for Maxwell’s Equations with a Nonlinear Boundary Condition

2015 ◽  
Vol 8 (4) ◽  
pp. 605-633
Author(s):  
Tong Kang ◽  
Ran Wang ◽  
Tao Chen ◽  
Huai Zhang
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Perfect Conductor ◽  
Fully Discrete ◽  
The Relationship ◽  
Nonlinear Degenerate ◽  
Element Method

AbstractIn this paper we present a fully discrete A-ø finite element method to solve Maxwell’s equations with a nonlinear degenerate boundary condition, which represents a generalization of the classical Silver-Müller condition for a non-perfect conductor. The relationship between the normal components of the electric field E and the magnetic field H obeys a power-law nonlinearity of the type H x n = n x (|E x n|α-1E x n) with α ∈ (0,1]. We prove the existence and uniqueness of the solutions of the proposed A-ø scheme and derive the error estimates. Finally, we present some numerical experiments to verify the theoretical result.

Nonconforming Mixed Finite Element Method for Time-dependent Maxwell's Equations with ABC

2016 ◽  
Vol 9 (2) ◽  
pp. 193-214
Author(s):  
Changhui Yao ◽  
Dongyang Shi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Absorbing Boundary Conditions ◽  
Time Dependent ◽  
Backward Euler ◽  
Element Method

AbstractIn this paper, a nonconforming mixed finite element method (FEM) is presented to approximate time-dependent Maxwell's equations in a three-dimensional bounded domain with absorbing boundary conditions (ABC). By employing traditional variational formula, instead of adding penalty terms, we show that the discrete scheme is robust. Meanwhile, with the help of the element's typical properties and derivative transfer skills, the convergence analysis and error estimates for semidiscrete and backward Euler fully-discrete schemes are given, respectively. Numerical tests show the validity of the proposed method.

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