Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled Klein-Gordon Equations

Abstract

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 $\mathcal{O}(h^2+∆t^2 )$ by using the error splitting technique and postprocessing interpolation. Numerical experiments are carried out to support our theoretical results.