非线性双相滞热传导方程的新混合元超收敛分析  

Superconvergence Analysis of a New Mixed Finite Element Method for Nonlinear Dual Phase Lagging Heat Conduction Equations

作　　者：赵艳敏[1,2] 石东伟[3] 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 [2]郑州大学数学与统计学院,河南郑州450001 [3]河南科技学院数学系,河南新乡453003

出　　处：《数学的实践与认识》2014年第5期269-274,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11101381);河南省高等学校青年骨干教师资助项目(2011GGJS-182);河南省教育厅自然科学基金项目(13A110741);许昌市科技计划项目(5015)

摘　　要：针对非线性双相滞热传导方程,建立了一种自由度少且自然满足B-B条件的新混合元逼近格式.在半离散格式下,基于双线性元的高精度结果,分别导出了原始变量的H^1模及中间变量的L^2模的超逼近性质,进而,借助于插值后处理算子,得到了原始及中间变量比传统误差高一阶的整体超收敛结果.A new mixed finite element approximate formulation is established for nonlinear dual phase lagging heat conduction equations, which can satisfy B-B condition automatically. Under semi-discrete scheme, the superclose properties of original variable in H1-norm and intermediate variable in L2- norm are derived based on high accuracy results of bilinear finite element, respectively. Moreover, the global superconvergence results of original variable and intermediate variable are obtained by use of interpolation postprocessing operators, which are one order higher than traditional error estimates.

关 键 词：非线性双相滞热传导方程 新混合元格式 双线性元 超逼近 超收敛 

分 类 号：O241.82[理学—计算数学]