(untitled) (Communications in Computational Physics, 2020)
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 O(τ^ r+1+h^k+12 ) 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.