非线性湿气迁移方程的超收敛分析  

Superconvergence Analysis of Nonlinear Moisture Migration Equations

作　　者：谢华朝 石东洋 XIE HUAZHAO;SHI DONGYANG(School of Mathematics and Information Science,Henan University of Economics and Law,Zhengzhou 450046,China;School of Mathematics and Information Sciences,Yantai University,Yantai 264005,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]烟台大学数学与信息科学学院,烟台264005

出　　处：《应用数学学报》2024年第3期498-516,共19页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(批准号:11671369,12071443)资助项目。

摘　　要：本文用混合有限元方法研究一般的非线性湿气迁移方程.利用双线性元Q_(11)和零阶Raviart-Thomas元(Q_(10)×Q_(01))证明方程的超收敛性.利用这两个单元插值算子的性质和平均值技巧,得到了方程半离散格式的O(h^(2))阶超收敛结果.对于方程线性化的Crank-Nicolson(C-N)全离散格式,得到了具有O(h^(2)+τ^(2))阶的超收敛结果,这里h是空间剖分参数,τ是时间步长.该方法说明如果线性化问题有超收敛性,那么对应的非线性问题有同样的超收敛性.最后,给出数值算例,证实了理论分析的正确性和方法的有效性.In this paper,the general nonlinear moisture migration equations are studied with a mixed finite element method.The superconvergence of the equations is proved by use of bilinear element Q_(11) and zero order Raviart-Thomas element(Q_(10)×Q_(01)).With the help of the interpolation operators of the above two elements and mean-value technique,the superconvergence results of order O(h^(2))are obtained for the semi-discrete scheme of the equations.For the linearized Crank-Nicolson(C-N)fully-discrete scheme,the superconvergence results of order O(h^(2)+τ^(2))are also derived,here h is the subdivision parameter,τ is the time step.This method shows that if the linearization problem has superconvergence,the corresponding nonlinear problem has the same superconvergence.Finally,a numerical example is provided to illustrate the correctness of the theoretical analysis and the feasibility of the proposed method.

关 键 词：非线性湿气迁移方程 混合有限元 线性化格式 超收敛分析 

分 类 号：O242.21[理学—计算数学]