A new error analysis of an explicit skeletal discontinuous Galerkin scheme for time-dependent Maxwell equations

This article focuses on the convergence analysis of second-order time-dependent Maxwell equations in conducting and non-conducting media. Firstly, the spatial discretization is made using a skeletal discontinuous Galerkin method, and then some essential tools are established to deduce the stability and error estimates. Under suitable regularity assumptions on initial data, stability and optimal convergence of the error are proved for the semi-discrete problem in a discretely defined $H\text{(curl)}$-norm. Next, temporal discretization is applied to the semi-discrete system by using the explicit Leap-frog schemes and optimal error bounds $O({\tau }^2+h^k)$, $k\ge 1$ is the degree of polynomial approximation, are achieved in the discrete energy norm. Finally, computational experiments are performed to validate the theoretical conclusions. Error analysis of explicit fully discrete schemes in polygonal/polyhedral meshes for the second-order Maxwell equations in a conducting media is missing in the literature, and we intend to fill this gap in the current article.