In 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 $L^2$-stability and error estimate of order $\mathcal{O}$($τ^ {r+1}$+$h^{k+\frac{1}{2}}$) 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.scpde14.35s}, url = {http://global-sci.org/intro/article_detail/cicp/11127.html} }