EQ^(rot)_1 Nonconforming Finite Element Method for Nonlinear Dual Phase Lagging Heat Conduction Equations  

作　　者：Yan-min Zhao Fen-ling Wang Dong-yang Shi 

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

出　　处：《Acta Mathematicae Applicatae Sinica》2013年第1期201-214,共14页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Nos. 10971203; 11101381);Tianyuan Mathe-matics Foundation of National Natural Science Foundation of China (No. 11026154);Natural Science Foundation of Henan Province (No. 112300410026);Natural Science Foundation of the Education Department of Henan Province (Nos. 2011A110020; 12A110021)

摘　　要：EQrot nonconforming finite element approximation to a class of nonlinear dual phase lagging heat conduction equations is discussed for semi-discrete and fully-discrete schemes. By use of a special property, that is, the consistency error of this element is of order O（h2） one order higher than its interpolation error O（h）, the superclose results of order O（h2） in broken Hi-norm are obtained. At the same time, the global superconvergence in broken Hi-norm is deduced by interpolation postprocessing technique. Moreover, the extrapolation result with order O（h4） is derived by constructing a new interpolation postprocessing operator and extrapolation scheme based on the known asymptotic expansion formulas of EQrot element. Finally, optimal error estimate is gained for a proposed fully-discrete scheme by different approaches from the previous literature.EQrot nonconforming finite element approximation to a class of nonlinear dual phase lagging heat conduction equations is discussed for semi-discrete and fully-discrete schemes. By use of a special property, that is, the consistency error of this element is of order O（h2） one order higher than its interpolation error O（h）, the superclose results of order O（h2） in broken Hi-norm are obtained. At the same time, the global superconvergence in broken Hi-norm is deduced by interpolation postprocessing technique. Moreover, the extrapolation result with order O（h4） is derived by constructing a new interpolation postprocessing operator and extrapolation scheme based on the known asymptotic expansion formulas of EQrot element. Finally, optimal error estimate is gained for a proposed fully-discrete scheme by different approaches from the previous literature.

关 键 词：nonlinear dual phase lagging heat conduction equations EQrot nonconforming finite element superclose and superconvergence EXTRAPOLATION semi-discrete and fully-discrete schemes 

分 类 号：O551.3[理学—热学与物质分子运动论] TP242[理学—物理]