scholarly journals Analysis and Application of Single Level, Multi-Level Monte Carlo and Quasi-Monte Carlo Finite Element Methods for Time-Dependent Maxwell's Equations with Random Inputs

2021 ◽  
Vol 29 (1) ◽  
pp. 211-236
Author(s):  
Xiang Wang
Keyword(s):  
Finite Element ◽  
Monte Carlo ◽  
Finite Element Methods ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Time Dependent ◽  
Random Inputs ◽  
Single Level ◽  
Quasi Monte Carlo ◽  
Multi Level

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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