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

• Main Authors: Xiaohui Hu, Pengzhan Huang, Xinlong Feng
• Format: Article
• Language: English
• Published: Vilnius Gediminas Technical University 2014-02-01
• Series: Mathematical Modelling and Analysis
• Subjects: Burgers’ equation; two-grid method; stable conforming finite element; Crank-Nicolson scheme; inf-sup condition
• Online Access: https://journals.vgtu.lt/index.php/MMA/article/view/3256

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.