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《山东大学学报(理学版)》 ›› 2026, Vol. 61 ›› Issue (4): 133-142.doi: 10.6040/j.issn.1671-9352.0.2024.006

• • 上一篇    

非线性Sobolev-Galpern型方程的超收敛分析

李素丽,谢华朝*   

  1. 河南财经政法大学数学与信息科学学院, 河南 郑州 450046
  • 发布日期:2026-04-08
  • 通讯作者: 谢华朝(1982— ),男,教授,博士,研究方向为偏微分方程及其应用. E-mail:hzhxie@126.com
  • 作者简介:李素丽(1982— ),女,讲师,硕士,研究方向为偏微分方程数值解. E-mail:20140097@huel.edu.cn*通信作者:谢华朝(1982— ),男,教授,博士,研究方向为偏微分方程及其应用. E-mail:hzhxie@126.com
  • 基金资助:
    国家自然科学基金资助项目(11671369)

Superconvergence analysis of nonlinear Sobolev-Galpern equations

LI Suli, XIE Huazhao*   

  1. School of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou 450046, Henan, China
  • Published:2026-04-08

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摘要： 用低阶混合有限元(Q11+Q01×Q10)研究非线性Sobolev-Galpern型方程。利用双线性元Q11及Q01×Q10元的高精度结果和平均值技巧,得到方程半离散格式的O(h2)阶超收敛结果。对于方程线性化的全离散格式,得到具有O(h2+τ2)阶的超收敛结果,其中h是空间剖分参数,τ是时间步长。最后,通过数值算例证实理论分析的正确性。

关键词: 非线性Sobolev-Galpern 型方程, 混合有限元, 线性化格式, 超收敛分析

Abstract: The nonlinear Sobolev-Galpern equations are studied with low order mixed finite element (Q11+Q01×Q10). By utilizing the high precision results of the finite element Q11+Q01×Q10, and mean-value technique, the superconvergence results of order O(h2)are obtained for the semi-discrete scheme of the equations. For the linearized fully discrete scheme, the superconvergence results of order O(h2+τ2)are also derived, here h is the subdivision parameter, τ is the time step. Finally, a numerical example is provided to confirm our theoretical analysis.

Key words: nonlinear Sobolev-Galpern equations, mixed finite element, linearized scheme, superconvergence analysis

中图分类号: 

  • O242.21
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