非线性湿气迁移方程H^1-Galerkin混合有限元的超逼近分析  

Superclose Analysis of a H^1-Galerkin Mixed Finite Element Method for Nonlinear Moisture Migration Equations

作　　者：谢华朝 李素丽 秦健[2] XIE Huazhao;LI Suli;QIN JlAN(College of Mathematics and Information Science,Henan University of Economics and Law,Zhengzhou 450046,China;Henan Provincial Party School,Zhengzhou 451000,China)

机构地区：[1]河南财经政法大学数学与信息科学学院,郑州450046 [2]河南省委党校,郑州451000

出　　处：《应用数学学报》2019年第6期813-829,共17页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11671369)资助项目

摘　　要：本文利用不完全双二次元QF和一阶BDFM元对一类非线性Sobolev-Galpern型的湿气迁移方程,建立了一个新的混合元逼近模式.利用这两个单元插值算子的特殊性质和平均值技巧,一方面,对半离散格式,证明了逼近格式解的存在唯一性.同时导出了原始变量在H1-模和中间变量在H(div)-模意义下具有O(h3)阶的超逼近性质.另一方面,对于线性化Crank-Nicolson(C-N)全离散格式,在没有网格比的要求下,导岀了具有0(/?+/)阶的超逼近结果.这里人是空间细分参数,亍是时间步长.In this article, H1-Galerkin mixed finite elemen t met hod for a kind of nonlinearmoisture migration equations is studied. A new mixed finite element pattern is developedwith incomplete biquadratic element and first *otdei BDFM element. On one hand,the existence and uniqueness of solutions about the semi-discrete approximation scheme areproved. With the help of the special proper ties of the interpolation operators of t hese twoelements and mean-value technique, the superclose results of order O(/z3) for the primitivevariable in H^norm and the intermediate variable in H(div)-norm are obtained. On theother hand, a linearized Crank-Nicolson fully discrete schemes with the unconditional supercloseproperty O{h3 +r2 are deduced. Here h is the subdivision parameter and t is thetime step.

关 键 词：湿气迁移方程 M-Galerkin 混合有限元方法 超逼近分析 

分 类 号：O242.21[理学—计算数学]