An implicit discontinuous Galerkin method is introduced to solve the timedomain
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(τ
p+1/2). Numerical results in both 2D and 3D
are provided to validate our theoretical prediction.