非线性修正Burgers方程的空间两重网格混合有限元方法

A Spatial Two-Grid Mixed Finite Element Method for Nonlinear Modified Burgers’ Equation

摘要: 本文研究二维非线性修正Burgers方程的高效数值求解问题，构造了一种基于Crank-Nicolson时间离散的空间两重网格混合有限元方法。进一步地，数值实验验证了所提出方法的有效性。计算结果显示，$u$ 的$L^2$ 误差具有约二阶收敛精度。同时，与单网格方法相比，两重网格方法在保持相近精度的基础上显著减少了计算时间。

Abstract: This paper investigates the efficient numerical solution of the two-dimensional nonlinear modified Burgers equation. A spatial two-grid mixed finite element method combined with the Crank-Nicolson time discretization is developed. Numerical experiments are further conducted to verify the effectiveness of the proposed method. The computational results demonstrate that the $L^2$ -norm error of $u$ achieves an approximately second-order convergence rate. Moreover, compared with the standard single-grid method, the proposed two-grid method significantly reduces the computational time while maintaining comparable numerical accuracy.