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

页码：1 / 17

页数：17

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