多尺度有限元法在分层网格上的边界层数值模拟

Numerical simulation of boundary layer on graded grid bymultiscale finite element method

针对二维奇异摄动问题的对流扩散方程,应用多尺度有限元法在分层网格上数值求解边界层现象.利用多尺度有限元的基函数承载微观摄动性态,在宏观尺度下仅用少量计算资源通过分层网格自适应地逼近边界层.数值模拟结果表明,该方法是有效的且能得到不依赖于摄动系数大小与稳定收敛的高精度结果.

As for a two-dimensional convection-diffusion equation in singularly perturbed problems,a multiscale finite element method based on graded grids is proposed for the boundary layers phenomena.The multiscale finite element basis functions are loaded with the microscopic perturbed behaviors,thus on a macroscopic scale with only a small amount of computational resources the method is capable of adaptively capturing the boundary layers by the graded grids.Numerical simulations show that the method is efficient,and high precision results with the properties of uniform convergence and numerical stability are fulfilled.