一类非线性非局部抛物问题的类Wilson非协调元分析
Quasi-Wilson Nonconforming Finite Element Analysis to a Class of Nonlinear and Nonlocal Parabolic Problems
王萍莉1
作者信息
- 1. 许昌学院 数理学院,河南 许昌 461000
- 折叠
摘要
主要研究在半离散格式下一类非线性非局部抛物问题的类Wilson非协调元逼近.当问题的精确解u∈H3(Ω)时,利用该单元相容误差在能量范数意义下可达到O(h2)阶(比其插值误差高一阶)的特殊性质,采用关于时间t的导数转移技巧,并结合双线性元的高精度分析和插值后处理技巧,得到了超逼近性质和整体超收敛结果.
Abstract
A Quasi-Wilson nonconforming finite element approximation is discussed for a class of nonlinear and nonlocal parabolic problems under semi-discrete schemes.The element has a special character that the con-sistency error can reach to order O(h2)in energy norm(one order higher than its interpolation error)when exact solution belongs to u∈H3(Ω).Using the special property,the derivative transfering technique with respect to the time t,and combined with the high precision analysis of bilinear element and interpolation post-processing technique,the superclose property and global superconvergence result are obtained.
关键词
非线性非局部抛物问题/类Wilson非协调元/高精度分析/超逼近超收敛Key words
nonlinear and nonlocal parabolic problems/Quasi-Wilson/high accuracy analysis/superclose and superconvergence引用本文复制引用
基金项目
河南省高等学校科技创新团队支持计划(23IRTSTHN08)
出版年
2024
NETL
NSTL
万方数据