Error analysis of a fully discrete discontinuous Galerkin alternating direction implicit discretization of a class of linear wave-type problems

Abstract This paper is concerned with the rigorous error analysis of a fully discrete scheme obtained by using central fluxes discontinuous Galerkin (dG) method in space and Peaceman–Rachford splitting time. We apply to general class wave-type problems show that resulting approximations as well derivatives thereof satisfy bounds order polynomial degree used dG discretization two In particular, considered includes, e.g., advection equation, acoustic wave Maxwell equations for which very efficient implementation possible via an alternating direction implicit splitting.