UNCONDITIONALLY SUPERCLOSE ANALYSIS OF A NEW MIXED FINITE ELEMENT METHOD FOR NONLINEAR PARABOLIC EQUATIONS

作     者：Dongyang Shi Fengna Yan Junjun Wang 

作者机构：School of Mathematics and StatisticsZhengzhou UniversityZhengzhou 450001China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2019年第37卷第1期

页      面：1-17页

核心收录：

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Natural Science Foundation of China (Grant Nos.11671369 11271340). 

主　　题：Nonlinear parabolic equation Mixed FEM Time-discrete and spatial-discrete systems τ-independent superelose results 

摘      要：This paper develops a framework to deal with the unconditional superclose analysis of nonlinear parabolic equation.Taking the finite dement pair Q11/Q01×Q10 as an example, a new mixed finite element method (FEM)is established and the r-independent superclose results of the original variable u in Hi-norm and the flux variable q=-a(u)■u in L^2- norm are deduced (τ is the temporal partition parameter).A key to our analysis is all error splitting technique,with which the time-discrete and the spatial-discrete systems are constructed,respectively.For the first system,tile boundedness of the temporal errors are obtained.For the second system,the spatial superclose results are presented unconditionally.while the previous literature always only obtain the convergent estimates or require certain time step conditions.Finally,some numerical results are provided to confirm the theoretical analysis,and show the efficiency of the proposed method.