Solving Maxwell's Equation in Meta-Materials by a CG-DG Method

2016 ◽  
Vol 19 (5) ◽  
pp. 1242-1264 ◽  
Author(s):  
Ziqing Xie ◽  
Jiangxing Wang ◽  
Bo Wang ◽  
Chuanmiao Chen
Keyword(s):  
Error Estimate ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Numerical Results ◽  
Time Dependent ◽  
Spatial Discretization ◽  
Maxwell’S Equation ◽  
Temporal Discretization ◽  
Dg Method ◽  
Theoretical Results

AbstractIn this paper, an approach combining the DG method in space with CG method in time (CG-DG method) is developed to solve time-dependent Maxwell's equations when meta-materials are involved. Both the unconditional L2-stability and error estimate of order are obtained when polynomials of degree at most r is used for the temporal discretization and at most k for the spatial discretization. Numerical results in 3D are given to validate the theoretical results.

Optimal L2 Error Estimates for the Interior Penalty DG Method for Maxwell’s Equations in Cold Plasma

2012 ◽  
Vol 11 (2) ◽  
pp. 319-334 ◽  
Author(s):  
Jichun Li
Keyword(s):  
Error Estimates ◽  
Discontinuous Galerkin ◽  
Maxwell’S Equations ◽  
Cold Plasma ◽  
Maxwell's Equations ◽  
Time Dependent ◽  
Interior Penalty ◽  
Fully Discrete ◽  
Tetrahedral Meshes ◽  
Dg Method

AbstractIn this paper, we consider an interior penalty discontinuous Galerkin (DG) method for the time-dependent Maxwell’s equations in cold plasma. In Huang and Li (J. Sci. Comput., 42 (2009), 321-340), for both semi and fully discrete DG schemes, we proved error estimates which are optimal in the energy norm, but sub-optimal in the L2-norm. Here by filling this gap, we show that these schemes are optimally convergent in the L2-norm on quasi-uniform tetrahedral meshes if the solution is sufficiently smooth.

scholarly journals Weak Galerkin methods for time-dependent Maxwell’s equations

2017 ◽  
Vol 74 (9) ◽  
pp. 2106-2124 ◽  
Author(s):  
Sidney Shields ◽  
Jichun Li ◽  
Eric A. Machorro
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Time Dependent ◽  
Galerkin Methods ◽  
Weak Galerkin

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.

The Electric Field in Maxwell's Equations

1978 ◽  
Vol 15 (2) ◽  
pp. 169-171 ◽  
Author(s):  
Z. L. Budrikis
Keyword(s):  
Electric Field ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Coulomb Force ◽  
Maxwell’S Equation ◽  
Ohm’S Law ◽  
Ohm's Law ◽  
Maxwell's Equation

The field E in Maxwell's equation curl E = – δB/δ t is limited to induction and Coulomb force. It does not extend to all phenomena that are included in E of Ohm's law, J = σE. Maxwell's equation would need another term to account for additional vorticity of the E in Ohm's law.

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