Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2017.81.89ZaghdaniAbdelhamid MohamedM. Ezzat El-MaghrabiA.I. 22017172Background: 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 Maxwells equations. Methodology: This study applied the discontinuous Galerkin method for approximating the electric field which is solution of a wave equation that derives from Maxwells equations in a tridimensional domain. Results: Some discrete inequalities on discontinuous spaces for Maxwells 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.]]>Cangiani, A., Z. Dong, E.H. Georgoulis and P. Houston,201550699725Houston, P., C. Schwab and E. Suli,20023921332163Wheeler, M.F.,197815152161Arnold, D.N.,198219742760Houston, P., I. Perugia and D. Schotzau,20032003pp: 785-794pp: 785-794Atcheson, T.R.,20152015Duvaut, G. and P.L. Lions,1976Pages: 367Pages: 367Zaghdani, A.,20062006Perugia, I. and D. Schotzau,200324311791214Zaghdani, A. and C. Daveau,20063422932Girault, V. and P.A. Raviart,1986Schwab, C.,1968Babuska, I. and M. Suri,198721199238Raviart, P.A. and J.M. Thomas,1983Cockburn, B., G.E. Karniadakis and C.W. Shu,20002000pp: 3-50pp: 3-50