A new family of mixed finite elements in IR3
Numerische Mathematik
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids
SIAM Journal on Numerical Analysis
Convergence Analysis of a Finite Volume Method for Maxwell's Equations in Nonhomogeneous Media
SIAM Journal on Numerical Analysis
Nodal high-order methods on unstructured grids
Journal of Computational Physics
Mixed Discontinuous Galerkin Approximation of the Maxwell Operator
SIAM Journal on Numerical Analysis
Interior penalty method for the indefinite time-harmonic Maxwell equations
Numerische Mathematik
SIAM Journal on Numerical Analysis
Optimal Discontinuous Galerkin Methods for Wave Propagation
SIAM Journal on Numerical Analysis
Discontinuous Galerkin Approximation of the Maxwell Eigenproblem
SIAM Journal on Numerical Analysis
Discontinuous Galerkin computation of the Maxwell eigenvalues on simplicial meshes
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
A Locally Divergence-Free Interior Penalty Method for Two-Dimensional Curl-Curl Problems
SIAM Journal on Numerical Analysis
A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
Optimal Discontinuous Galerkin Methods for the Acoustic Wave Equation in Higher Dimensions
SIAM Journal on Numerical Analysis
Superconvergence of mixed finite element approximations to 3-D Maxwell's equations in metamaterials
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
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In this paper, a new type of staggered discontinuous Galerkin methods for the three dimensional Maxwell's equations is developed and analyzed. The spatial discretization is based on staggered Cartesian grids so that many good properties are obtained. First of all, our method has the advantages that the numerical solution preserves the electromagnetic energy and automatically fulfills a discrete version of the Gauss law. Moreover, the mass matrices are diagonal, thus time marching is explicit and is very efficient. Our method is high order accurate and the optimal order of convergence is rigorously proved. It is also very easy to implement due to its Cartesian structure and can be regarded as a generalization of the classical Yee's scheme as well as the quadrilateral edge finite elements. Furthermore, a superconvergence result, that is the convergence rate is one order higher at interpolation nodes, is proved. Numerical results are shown to confirm our theoretical statements, and applications to problems in unbounded domains with the use of PML are presented. A comparison of our staggered method and non-staggered method is carried out and shows that our method has better accuracy and efficiency.