scholarly journals Correction to: Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations

2021 ◽  
Author(s):  
Jörg Nick ◽  
Balázs Kovács ◽  
Christian Lubich
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Fully Discrete

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.

Space-Time Discontinuous Galerkin Method for Maxwell’s Equations

2013 ◽  
Vol 14 (4) ◽  
pp. 916-939 ◽  
Author(s):  
Ziqing Xie ◽  
Bo Wang ◽  
Zhimin Zhang
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Time Step ◽  
Fully Discrete ◽  
Temporal Domain ◽  
Grid Points ◽  
Spatial Approximation

AbstractA fully discrete discontinuous Galerkin method is introduced for solving time-dependent Maxwell’s equations. Distinguished from the Runge-Kutta discontinuous Galerkin method (RKDG) and the finite element time domain method (FETD), in our scheme, discontinuous Galerkin methods are used to discretize not only the spatial domain but also the temporal domain. The proposed numerical scheme is proved to be unconditionally stable, and a convergent rate is established under the L2-norm when polynomials of degree atmost r and k are used for temporal and spatial approximation, respectively. Numerical results in both 2-D and 3-D are provided to validate the theoretical prediction. An ultra-convergence of order in time step is observed numerically for the numerical fluxes w.r.t. temporal variable at the grid points.

Implicit DG Method for Time Domain Maxwell’s Equations Involving Metamaterials

2015 ◽  
Vol 7 (6) ◽  
pp. 796-817 ◽  
Author(s):  
Jiangxing Wang ◽  
Ziqing Xie ◽  
Chuanmiao Chen
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Time Domain ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Fully Discrete ◽  
Integral Differential Equations ◽  
The Time Domain ◽  
Spatial Approximation

AbstractAn implicit discontinuous Galerkin method is introduced to solve the time-domain Maxwell’s equations in metamaterials. The Maxwell’s equations in metamaterials are represented by integral-differential equations. Our scheme is based on discontinuous Galerkin method in spatial domain and Crank-Nicolson method in temporal domain. The fully discrete numerical scheme is proved to be unconditionally stable. When polynomial of degree at most p is used for spatial approximation, our scheme is verified to converge at a rate of O(τ2+hp+1/2). Numerical results in both 2D and 3D are provided to validate our theoretical prediction.

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.

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.

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