(untitled) (Advances in Applied Mathematics and Mechanics, 2023)
In this paper, we consider the energy conserving numerical scheme for coupled nonlinear Klein-Gordon equations. We propose energy conserving finite element method and get the unconditional superconvergence result O(h^2+∆t^2 ) by using the error splitting technique and postprocessing interpolation. Numerical experiments are carried out to support our theoretical results.