Two-Grid Method for Burgers' Equation by a New Mixed Finite Element Scheme

被引：10
作者：
Hu, Xiaohui [1 ]
Huang, Pengzhan [1 ]
Feng, Xinlong [1 ]
机构：
[1] Xinjiang Univ, Urumqi 830046, Peoples R China
来源：
MATHEMATICAL MODELLING AND ANALYSIS | 2014年 / 19卷 / 01期
基金：
中国博士后科学基金;
关键词：
Burgers' equation; two-grid method; stable conforming finite element; Crank-Nicolson scheme; inf sup condition; SEMILINEAR ELLIPTIC-EQUATIONS; TIME-STEPPING STRATEGY; DIFFUSION EQUATIONS;
D O I：
10.3846/13926292.2014.892902
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article, we present two-grid stable mixed finite element method for the 2D Burgers' equation approximated by the P-0(2) - P-1 pair which satisfies the inf-sup condition. This method consists in dealing with the nonlinear system on a coarse mesh with width H and the linear system on a fine mesh with width h << H by using Crank-Nicolson time-discretization scheme. Our results show that if we choose H-2 = h this method can achieve asymptotically optimal approximation. Error estimates are derived in detail. Finally, numerical experiments show the efficiency of our proposed method and justify the theoretical results.
引用
收藏
页码：1 / 17
页数：17
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