TGMFE algorithm combined with some time second-order schemes for nonlinear fourth-order reaction diffusion system

被引：5

作者：

Yin, Baoli ^{[1
]}

Liu, Yang ^{[1
]}

Li, Hong ^{[1
]}

He, Siriguleng ^{[1
]}

Wang, Jinfeng ^{[2
]}

机构：

[1] Inner Mongolia Univ, Sch Math Sci, Hohhot 010021, Peoples R China

[2] Inner Mongolia Univ Finance & Econ, Sch Stat & Math, Hohhot 010070, Peoples R China

来源：

RESULTS IN APPLIED MATHEMATICS | 2019年 / 4卷

基金：

中国国家自然科学基金;

关键词：

Second-order; scheme; Nonlinear fourth-order reaction diffusion equation; TGMFE algorithm; Stability; Error estimates; FINITE-ELEMENT METHODS; 2-GRID METHOD; APPROXIMATIONS; EQUATIONS;

D O I：

10.1016/j.rinam.2019.100080

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, a two-grid mixed finite element (TGMFE) method with some secondorder time discrete schemes is developed for numerically solving nonlinear fourth-order reaction diffusion equation. The two-grid MFE method is used to speed up the solution in space, and some second-order. schemes are adopted to discretize the time derivative. The TGMFE method is formed by two main steps: a nonlinear MFE system based on the space coarse grid is firstly solved by the iterative algorithm, then a linearized MFE system on the fine grid is solved. Here, the stability and a priori error estimates in L-2-norm for both nonlinear Galerkin MFE system and TGMFE scheme are proved. Finally, some convergence results are presented for both nonlinear Galerkin MFE system and TGMFE scheme to verify our theoretical analysis. (C) 2019 The Author(s). Published by Elsevier B.V.

引用

页数：17

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