Solving Maxwell's Equation in Meta-Materials by a CG-DG Method (Communications in Computational Physics, 2020)
In this paper, an approach combining the DG method in space with CGmethod in time (CG-DG method) is developed to solve time-dependent Maxwell'sequations when meta-materials are involved. Both the unconditional $L^2$-stability anderror estimate of order $\mathcal{O}$($τ^ {r+1}$+$h^{k+\frac{1}{2}}$) are obtained when polynomials of degree atmost 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.