Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled Klein-Gordon Equations (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 elementmethod and get the unconditional superconvergence result $\mathcal{O}(h^2+∆t^2)$ by using the error splitting technique and postprocessing interpolation. Numerical experiments arecarried out to support our theoretical results.