一类非线性抛物方程H^1-Galerkin混合有限元方法的高精度分析  

Superconvergence Analysis of an H^1-Galerkin Mixed Finite Element Method for Nonlinear Parabolic Equation

作　　者：王俊俊 杨晓侠 Wang Junjun;Yang Xiaoxia(School of Mathematics and Statistics, Pingdingshan University, Henan Pingdingshan 467000)

机构地区：[1]平顶山学院数学与统计学院

出　　处：《数学物理学报（A辑）》2019年第4期894-908,共15页Acta Mathematica Scientia

基　　金：国家自然科学基金(11671369);平顶山学院博士启动基金(PXY-BSQD-2019001)和平顶山学院培育基金(PXY-PYJJ-2019006)~~

摘　　要：研究了非线性抛物方程的H^1-Galerkin混合有限元方法.利用双线性元及零阶Raviart-Thomas元在不提高原始解正则性的前提下,创新性的使用分裂技巧等讨论了半离散格式下和Euler全离散格式下的关于原始变量u的H^1(Ω)模及流量p=▽u的H(div;Ω)模的超逼近性质.数值算例证明了理论的正确性.Nonlinear parabolic equation is studied by H^1-Galerkin mixed finite element method.The bilinear element and the zero-order Raviart-Thomas elements are utilized to discuss superclose properties of the original variable u in H^1(Ω)and the flux p =▽u in H(div;Ω)under the semi-discrete scheme and Euler fully-discrete scheme.During the process,the splitting technique is used and the regularity of u and p are not improved.The numerical example confirm the theory.

关 键 词：非线性抛物方程 H1-Galerkin混合有限元方法 半离散格式和Euler全离散格式 超逼近性质 

分 类 号：O242.21[理学—计算数学]