非线性色散耗散波动方程双线性元新的高精度估计  

New high accurary estiments of bilinear element fornonlinear dispersion-disspative wave equations

作　　者：李玲 李秋红 兰奇逊 Li Ling;Li Qiuhong;Lan Qixun(School of Mathematics&Physics,Henan University of Urban Construction,Pingdingshan 467036,China)

机构地区：[1]河南城建学院数理学院,河南平顶山467036

出　　处：《河南师范大学学报（自然科学版）》2021年第4期24-29,共6页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学青年基金(61503122)。

摘　　要：主要研究具有局部Lipschitz连续非线性项的色散耗散波动方程双线性元新的高精度估计.对于半离散格式,利用插值与投影相结合的思想,在精解u,u t∈H^(2)(Ω)较弱的正则假设下,导出了H 1模意义下超逼近性,而以往文献在u,u t,u tt∈H^(2)(Ω)时却只能得到最优误差估计.进一步地,当u∈H^(3)(Ω)时,利用插值后处理技巧给出了整体超收敛结果,但不要求u t,u tt∈H^(3)(Ω),进而改善以往文献的结果.最后,建立了一个全离散逼近格式并研究了其解的超逼近性.This paper mainly studies the new high-precision estimates of the bilinear element for the dispersion wave equations with local Lipschitz continuous nonlinear term.In the semi-discrete scheme,the idea of combining interpolation and projection is used to get the superclose property under weaker regular assumption of u,u t∈H^(2)(Ω),but in the previous literature only optimal error estimate can be deduced.Further,based on interpolation post-processing techniques,the global super-convergence result is obtained when u∈H^(3)(Ω)instead of u,u t,u tt∈H^(3)(Ω).Finally,a fully discrete approximation scheme is established and a superclose estimate of its solution is investigated.

关 键 词：非线性色散耗散波动方程 双线性元 半离散和全离散格式 插值与投影结合 超逼近和超收敛估计 

分 类 号：O242.21[理学—计算数学]