抛物型拟线性积分微分方程基于扩展混合有限元的两层网格离散方法  

Two-grid Methods Based on Expanded Mixed Finite Element for Parabolic Semi-linear Integro-Differential Equations

作　　者：曾国艳 陈罗平 付雪梅 ZENG Guoyan;CHEN Luoping;FU Xuemei(School of Mathematics,Southwest Jiaotong University,Chengdu 611756,Sichuan)

机构地区：[1]西南交通大学数学学院,四川成都611756

出　　处：《四川师范大学学报（自然科学版）》2021年第6期784-791,共8页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金青年项目(11501473)。

摘　　要：为处理方程的拟线性性质,采用基于扩展混合有限元的两层网格离散方法研究拟线性抛物型积分微分方程.相对于经典的两层网格算法,基于扩展混合有限元方法的两层网格算法包含2步.在粗网格上,求解基于显式欧拉格式的线性问题;在细网格上,通过将非线性项基于粗网格解进行Taylor展开,从而求解一个线性化的方程组.理论和数值结果显示:当粗细网格步长满足h=H2时,该离散方法具有最优的收敛阶.In this paper,we present a two-grid algorithm for semi-linear parabolic integro-differential equations,based on expanded mixed finite element method,to deal with the semi-linear properties of the equation. Compared with the classical two-grid algorithm,the two-grid algorithm in this paper consists of two steps. They are the linear problem based on the explicit Euler scheme is solved on the coarse grid and the nonlinear term is linearized by Taylor expansion based on the coarse grid solution on the fine grid. Theoretical and numerical results show that the discrete method has the optimal convergence order if the mesh sizes satisfy h =H^(2).

关 键 词：两重网格算法 超收敛性 先验误差估计 拟线性抛物型积分微分方程 扩展混合有限元 

分 类 号：O241.82[理学—计算数学]