New high accurary estiments of bilinear element fornonlinear dispersion-disspative wave equations
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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∈H2(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∈H2(Ω)时却只能得到最优误差估计.进一步地,当u∈H3(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∈H3(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∈H2(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∈H3(Ω)instead of u,u t,u tt∈H3(Ω).Finally,a fully discrete approximation scheme is established and a superclose estimate of its solution is investigated.
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：
河南城建学院数理学院
出处：
《betway官方app 学报：自然科学版》 CAS 北大核心 2021年第4期24-29,共6页
基金：
国家自然科学青年基金(61503122)。
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
nonlinear dispersion and dissipation wave equation bilinear element semi-discrete and fully discrete schemes combination of interpolation and projection superclose and superconvergent estimetes
分类号：
O242.21 [理学—计算数学]
