A two-grid finite element method for nonlinear parabolic integro-differential equations
A two-grid finite element method for nonlinear parabolic integro-differential equations
复制标题
非线性抛物型积分微分方程的二网格有限元法
DOI：
10.1080/00207160.2018.1548699
复制
发表时间：
2019
影响因子：
1.8
通讯作者：
Zhang Yuanyuan
中科院分区：
文献类型：
--
作者：
Chen Chuanjun;Zhang Xiaoyan;Zhang Guodong;Zhang Yuanyuan
摘要本文给出了一类二维非线性抛物型积分-微分方程解的两重网格有限元方法。我们在网格尺寸为H的粗网格空间上求解一个完全非线性系统，得到精确解的一个粗略近似，然后在网格尺寸为h的细网格空间上求解相应的线性化问题，得到了空间半离散两网格有限元的最优范数误差估计。最后给出了算例，验证了该方法的有效性。
ABSTRACT In this paper, we present a two-grid finite element method (FEM) for a two-dimensional nonlinear parabolic integro-differential equation. We solve a fully nonlinear system on a coarse grid space with a grid size H and derive a rough approximation of the exact solution, and then solve the corresponding linearized problem on a fine grid space with a grid size h. The optimal error estimates in -norm are obtained for spatially the semidiscrete two-grid FEM. Finally, numerical examples are given to testify the efficiency of the method.