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

Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled Klein-Gordon Equations
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Year:    2023

Author:    Ming Cui, Yanfei Li, Changhui Yao

Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 3 : pp. 602–622

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2021-0261

Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 3 : pp. 602–622

Published online:    2023-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

Keywords:    Energy conserving the nonlinear coupled Klein-Gordon equations unconditional superconvergence result postprocessing interpolation finite element method.

Author Details

Ming Cui

Yanfei Li

Changhui Yao

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