Abstract: Background: The discontinuous Galerkin method for the approximation of a partial differential equation solution has some advantages comparing to the classical finite element method. Objective: This study aimed to provide a numerical approximation of the wave equation solution derived from Maxwell’s equations. Methodology: This study applied the discontinuous Galerkin method for approximating the electric field which is solution of a wave equation that derives from Maxwell’s equations in a tridimensional domain. Results: Some discrete inequalities on discontinuous spaces for Maxwell’s equations were presented and a discontinuous Galerkin method for the numerical approximation of the solution of the wave equation was analyzed. Its hp-analysis was carried out and error estimates that were optimal in the mesh size and slightly suboptimal in the approximation degree were obtained. The DG spatial discretization was augmented with the second order Newmark scheme in time and some numerical results were obtained. Conclusion: The results of the study can be applied for approximating solutions of several partial differential equations.