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

• 来源期刊: 计算数学（英文版）
• 关键词: Nonlinear parabolic equation Mixed FEM Time-discrete and spatial-discrete systems τ-independent superclose results.
• 年，卷（期）: 2019,（1）
• 页码范围: 1-17
• 页数: 17页
• 语种: 英文
• DOI: 10.4208/jcm.1707-m2016-0718

摘要

This paper develops a framework to deal with the unconditional superclose analysis of nonlinear parabolic equation.Taking the finite element pair Q11/Q01 × Q10 as an example,a new mixed finite element method (FEM) is established and the τ-independent superclose results of the original variable u in H1-norm and the flux variable (q)=-a(u)▽u in L2-norm are deduced (T is the temporal partition parameter).A key to our analysis is an error splitting technique,with which the time-discrete and the spatial-discrete systems are constructed,respectively.For the first system,the 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.