Superconvergence Analysis and Extrapolation of Quasi-Wilson Nonconforming Finite Element Method for Nonlinear Sobolev Equations  

作　　者：Dong-yang SHI Fen-ling WANG Yan-min ZHAO 

机构地区：[1]Department of Mathematics, Zhengzhou University [2]School of Mathematics and Statistics, Xuchang University

出　　处：《Acta Mathematicae Applicatae Sinica》2013年第2期403-414,共12页应用数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant Nos. 10971203; 11101381; 11271340);Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20094101110006);Tianyuan Mathematics Foundation of the National Natural Science Foundation of China(Grant No. 11026154);the Natural Science Foundation of Henan Province (Grant Nos. 112300410026; 122300410266)

摘　　要：Quasi-Wilson nonconforming finite element approximation for a class of nonlinear Sobolev equa- tions is discussed on rectangular meshes. We first prove that this element has two special characters by novel approaches. One is that （Vh（U -- Ihu）,VhVh）h may be estimated as order O（h2） when u E H3（Ω）, where Iuu denotes the bilinear interpolation of u, vh is a polynomial belongs to quasi-Wilson finite element space and △h denotes the piecewise defined gradient operator, h is the mesh size tending to zero. The other is that the consistency error of this element is of order O（h2）/O（h3） in broken Hi-norm, which is one/two order higher than its interpolation error when u ε Ha（Ω）/H4 （（1）. Then we derive the optimal order error estimate and su- perclose property via mean-value method and the known high accuracy result of bilinear element. Furthermore, we deduce the global superconvergence through interpolation post processing technique. At last, an extrapola- tion result of order O（h3）, two order higher than traditional error estimate, is obtained by constructing a new suitable extrapolation scheme.Quasi-Wilson nonconforming finite element approximation for a class of nonlinear Sobolev equa- tions is discussed on rectangular meshes. We first prove that this element has two special characters by novel approaches. One is that （Vh（U -- Ihu）,VhVh）h may be estimated as order O（h2） when u E H3（Ω）, where Iuu denotes the bilinear interpolation of u, vh is a polynomial belongs to quasi-Wilson finite element space and △h denotes the piecewise defined gradient operator, h is the mesh size tending to zero. The other is that the consistency error of this element is of order O（h2）/O（h3） in broken Hi-norm, which is one/two order higher than its interpolation error when u ε Ha（Ω）/H4 （（1）. Then we derive the optimal order error estimate and su- perclose property via mean-value method and the known high accuracy result of bilinear element. Furthermore, we deduce the global superconvergence through interpolation post processing technique. At last, an extrapola- tion result of order O（h3）, two order higher than traditional error estimate, is obtained by constructing a new suitable extrapolation scheme.

关 键 词：nonlinear Sobolev equations quasi-Wilson element superclose and superconvergence extrapola-tion 

分 类 号：O241.82[理学—计算数学] TN912.26[理学—数学]