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

作　　者：王萍莉[1] WANG Pingli(School of Science,Xuchang University,Xuchang 461000,China)

机构地区：[1]许昌学院数理学院,河南许昌461000

出　　处：《许昌学院学报》2024年第2期1-6,共6页Journal of Xuchang University

基　　金：河南省高校科技创新团队支持计划(23IRTSTHN08)。

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∈H^(3)(Ω)时,利用该单元相容误差在能量范数意义下可达到O(h^(2))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.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 consistency error can reach to order O(h^(2))in energy norm(one order higher than its interpolation error)when exact solution belongs to u∈H^(3)(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 

分 类 号：O241[理学—计算数学]