非线性Klein-Gordon方程的最低阶混合元超收敛分析新模式  

A New Scheme of the Lowest Order Mixed Element Superconvergence Analysis for Nonlinear Klein-Gordon Equations

作　　者：樊明智[1] 王芬玲[1] 

机构地区：[1]许昌学院数学与统计学院,河南许昌461000

出　　处：《许昌学院学报》2016年第5期1-9,共9页Journal of Xuchang University

基　　金：河南省教育厅自然科学基金项目(14A110009);河南省高等学校重点科研项目(16A110022);许昌市科技发展计划项目(1504004)

摘　　要：针对一类非线性Klein-Gordon方程利用最简单的双线性元Q_(11)及Q_(01)×Q_(10)元建立了最低阶且自然满足Brezzi-Babuska条件的混合元逼近格式.基于双线性元的积分恒等式结果,建立了插值与Riesz投影之间的超收敛估计,再结合Q_(01)×Q_(10)元的高精度分析结果和插值后处理技术,在半离散和全离散格式下,导出了关于原始变量u和流量p分别在H^1模和L^2模意义下单独利用插值或Riesz投影所无法得到的超逼近性和超收敛结果.With help of the bilinear element Q11 and Q01× Q10 element,the lowest order new mixed finite element scheme for nonlinear Klein-Gordon equations is proposed,which can satisfy Brezzi-Babuska condition antomatically on anisotropic meshes. Based on integral indentity result of bilinear element,a superconvergence estimate between the interpolation and Riesz projection,with the high accuracy analysis method of Q01× Q10 element and nterpolation post-processing technique,the superclose properties and superconvergence results of the orginal variable u and flux variable in H^1-norm and L^2-norm for semi-discrete and fully-discrete schemes can he deduced,which can＇t be deduced by the interpolation and Riesz projection alone.

关 键 词：非线性KLEIN-GORDON方程 超逼近性和超收敛结果 混合有限元新模式 半离散和全离散格式 

分 类 号：O242.21[理学—计算数学]