Fully discrete finite element approaches for time-dependent Maxwell's equations

1999 ◽  
Vol 82 (2) ◽  
pp. 193-219 ◽  
Author(s):  
P. Ciarlet, Jr ◽  
Jun Zou
Keyword(s):  
Finite Element ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Time Dependent ◽  
Fully Discrete ◽  
Discrete Finite Element

Finite Element Analysis of Maxwell’s Equations in Dispersive Lossy Bi-Isotropic Media

2013 ◽  
Vol 5 (04) ◽  
pp. 494-509 ◽  
Author(s):  
Yunqing Huang ◽  
Jichun Li ◽  
Yanping Lin
Keyword(s):  
Finite Element ◽  
Existence And Uniqueness ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Practical Implementation ◽  
Element Analysis ◽  
Fully Discrete ◽  
Isotropic Media ◽  
Discrete Finite Element ◽  
Finite Element Schemes

AbstractIn this paper, the time-dependent Maxwell’s equations used to modeling wave propagation in dispersive lossy bi-isotropic media are investigated. Existence and uniqueness of the modeling equations are proved. Two fully discrete finite element schemes are proposed, and their practical implementation and stability are discussed.

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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