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Volume 15, Issue 3
Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled Klein-Gordon Equations

Ming Cui, Yanfei Li & Changhui Yao

Adv. Appl. Math. Mech., 15 (2023), pp. 602-622.

Published online: 2023-02

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  • 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.

  • AMS Subject Headings

65N06, 65B99

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COPYRIGHT: © Global Science Press

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@Article{AAMM-15-602, author = {Cui , MingLi , Yanfei and Yao , Changhui}, title = {Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled Klein-Gordon Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2023}, volume = {15}, number = {3}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2021-0261}, url = {http://global-sci.org/intro/article_detail/aamm/21443.html} }
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.

Ming Cui, Yanfei Li & Changhui Yao. (2023). Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled Klein-Gordon Equations. Advances in Applied Mathematics and Mechanics. 15 (3). 602-622. doi:10.4208/aamm.OA-2021-0261
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