TY - JOUR T1 - Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled Klein-Gordon Equations AU - Cui , Ming AU - Li , Yanfei AU - Yao , Changhui JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 602 EP - 622 PY - 2023 DA - 2023/02 SN - 15 DO - http://doi.org/10.4208/aamm.OA-2021-0261 UR - https://global-sci.org/intro/article_detail/aamm/21443.html KW - Energy conserving, the nonlinear coupled Klein-Gordon equations, unconditional superconvergence result, postprocessing interpolation, finite element method. AB -

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.