基于Crank-Nicolson差分法的KdVB方程有限元解的误差分析  

Error analysis of finite element solution of KdVB equation based on Crank-Nicolson difference method

作　　者：姚富霞 YAO Fuxia(College of Science,Yanbian University,Yanji 133002,China)

机构地区：[1]延边大学理学院,吉林延吉133002

出　　处：《延边大学学报（自然科学版）》2022年第1期19-24,共6页Journal of Yanbian University（Natural Science Edition）

摘　　要：讨论了KdVB方程近似解的误差估计.首先,利用Crank-Nicolson差分法对KdVB方程的时间变量进行离散,由此得到了KdVB方程全离散的H^(1)误差估计.其次,基于特征正交分解(POD)方法得到了KdVB方程的降维模型;最后,根据Crank-Nicolson差分法对降维模型的时间变量进行离散,由此得到了降维模型的H^(1)误差估计.The error estimation of the approximate solution of the KdVB equation is discussed.Firstly,the time variables of the KdVB equation are discretized by the Crank-Nicolson difference method,and the H1 error estimation of the full discretization of the KdVB equation is obtained.Secondly,the dimensionality reduction model of the KdVB equation is obtained based on the characteristic orthogonal decomposition(POD)method;Finally,the time variables of the reduced dimension model are discretized according to the Crank-Nicolson difference method,and the H1error estimation of the reduced dimension model is obtained.

关 键 词：KdVB方程 Crank-Nicolson差分法 有限元解 误差分析 

分 类 号：O241.1[理学—计算数学]