The mixed finite element method for analysis of nonlinear time dependent eddy current field

1992 ◽  
Vol 28 (2) ◽  
pp. 1201-1203
Author(s):  
Wang Xin-Wei ◽  
Fang Zheng-Hu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Eddy Current ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Time Dependent ◽  
Current Field ◽  
Element Method

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.

An Oseen-Type Post-Processed Finite Element Method Based on a Subgrid Model for the Time-Dependent Navier–Stokes Equations

2019 ◽  
Vol 17 (04) ◽  
pp. 1950002
Author(s):  
Qihui Zhang ◽  
Yueqiang Shang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stokes Equations ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Time Dependent ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Subgrid Model ◽  
Element Method

An Oseen-type post-processed mixed finite element method based on a subgrid model is presented for the simulation of time-dependent incompressible Navier–Stokes equations. This method first solves a subgrid stabilized nonlinear Navier–Stokes system on a mesh of size [Formula: see text] to obtain an approximate solution pair [Formula: see text] at the given final time [Formula: see text], and then post-processes the solution [Formula: see text] by solving a stabilized Oseen problem on a finer mesh or in higher-order finite element spaces. We prove stability of the stabilized method, derive error estimates for the post-processed solutions, give some numerical results to verify the theoretical predictions and demonstrate the effectiveness of the proposed method.

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