Share:


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

Abstract

In this article, we present two-grid stable mixed finite element method for the 2D Burgers’ equation approximated by the -P1 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 H2 = 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.

Keyword : Burgers’ equation, two-grid method, stable conforming finite element, Crank-Nicolson scheme, inf-sup condition

How to Cite
Hu, X., Huang, P., & Feng, X. (2014). Two-Grid Method for Burgers’ Equation by a New Mixed Finite Element Scheme. Mathematical Modelling and Analysis, 19(1), 1-17. https://doi.org/10.3846/13926292.2014.892902
Published in Issue
Feb 20, 2014
Abstract Views
128
PDF Downloads
92
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.