黏弹性方程的Wilson元收敛性分析  

Convergence Analysis of Wilson Element for Viscoelasticity Type Equations

作　　者：杨晓侠 李永献 YANG Xiaoxia;LI Yongxian(School of Mathematics and Statistics, Pingdingshan University, Pingdingshan 467000, China;Henan University of Urban Construction, Pingdingshan 467036, China)

机构地区：[1]平顶山学院数学与统计学院,河南平顶山467000 [2]河南城建学院数理学院,河南平顶山467036

出　　处：《应用数学》2018年第3期513-521,共9页Mathematica Applicata

基　　金：国家自然科学基金(11271340;11671369);河南省科技计划项目(162300410082);河南省高等学校重点科研项目(16B110002)

摘　　要：对一类黏弹性方程利用Wilson元提出新的半离散和全离散逼近格式.基于单元的性质,通过定义新的双线性型,在不需要外推和插值后处理技术的前提下,分别得到了比传统的H^1-范数更大的模意义下相应的O(h^2)阶和O(h^2+τ~2)阶的误差分析结果,正好比通常的关于Wilson元的误差估计高出一阶.这里,h,τ表示空间剖分参数和时间步长.In this paper, with the help of the Wilson element, new semi-discrete and fully-discrete schemes are proposed for viscoelasticity type equations. Based on the properties of the element, through defining a new bilinear form, without using the technique of extrapolation and interpolated postprocessing,in the norm which is stronger than the usual H^1-norm, the convergence results with order O（h^2）/O（h^2＋τ^2）for the primitive solution are obtained for the corresponding schemes, respectively. The above results are just one order higher than the usual error estimates of the Wilson element. Here, h and τ are parameters of the subdivision in space and time step, respectively.

关 键 词：黏弹性方程 WILSON元 半离散和全离散格式 收敛性 

分 类 号：O242.21[理学—计算数学]