拟线性双曲方程类Wilson非协调元的高精度分析  

High Accuracy Analysis of the Nonconforming Quasi-Wilson Element Solution to Quasi-Linear Hyperbolic Equations

作　　者：吴志勤[1] 石东伟[2] 王芬玲[1] 石东洋[3] 

机构地区：[1]许昌学院数学与统计学院,河南许昌461000 [2]河南科技学院数学系,河南新乡453003 [3]郑州大学数学系,河南郑州450052

出　　处：《数学的实践与认识》2012年第10期192-198,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10671184;10971203);国家自然科学基金数学天元基金(11026154);高等学校博士学科点专项基金(20094101110006);河南省教育厅自然科学基金(2010A110018)

摘　　要：主要研究类Wilson元对拟线性双曲方程的逼近.首先证明了当问题的解u∈H^3(Ω)或u∈H^4(Ω)时,u与其双线性插值之差的梯度与类Wilson元空间任意元素的梯度,在分片意义下的内积可以达到O(h^2)这一重要结论.其次运用能量模意义下该元的非协调误差可以分别达到O(h^2)/O(h^3),即比插值误差高一阶/二阶这一性质,并利用对时间t的导数转移技巧,结合双线性元的高精度结果及插值后处理技术,获得了O(h^2)阶的超逼近性和整体超收敛性,从而进一步拓广了该元的应用范围.In this paper,quasi-Wilson finite element approximation is mainly studied for quasi-linear hyperbolic equations.First,an important conclusion is proven that the gradient of the difference between u and its bilinear interpolation and the gradient of the any element in quasi-Wilson space can be estimated with the order of O（h^2）in the sense of inner product piecewisely,when the solution u belongs to H^3（Ω） or H^4（Ω）.Then,by using the special property of the element that the consistency error can be estimated with order O（h^2）/O（h^3） in the energy,which is one/two order higher than the interpolation error,by making the transformation of the derivate with respect to time t,and according high accuracy analysis of bilinear element and post-processing techniques,the superclose property and superconvergence with order O（h^2）are derived.Therefore,the applicated scope of the element would be broadened.

关 键 词：高精度分析 拟线性双曲方程 类WILSON元 超收敛 

分 类 号：O175.27[理学—数学]