Optimal error estimate of a decoupled conservative local discontinuous Galerkin method for the Klein-Gordon-Schrödinger equations

In this paper, we propose a decoupled local discontinuous Galerkin method for solving the Klein-Gordon-Schrödinger (KGS) equations. The KGS equations is a model of the Yukawa interaction of complex scalar nucleons and real scalar mesons. The advantage of our scheme is that the computation of the nucleon and meson field is fully decoupled, so that it is especially suitable for parallel computing. We present the conservation property of our fully discrete scheme, including the energy and Hamiltonian conservation, and establish the optimal error estimate.