一维摄动边界层在优化网格的一致收敛多尺度有限元计算

Uniform convergence of multiscale finite element computation on optimal meshes for one-dimensional perturbed boundary layers

研究含极小摄动参数的一维对流扩散方程,应用多尺度有限元的高效计算格式求其数值解.构造的多尺度基函数能细致模拟边界层,迭代的自适应优化网格能精确逼近过渡点,通过Matlab模块化编程,从而在宏观尺度节省计算消耗,得到了范数度量下的一致收敛精确化模拟.

For a one-dimensional convection-diffusion equation with an extremely small perturbed parameter,a multiscale finite element scheme is proposed for its efficient numerical solution.The multiscale basis functions are able to simulate the boundary layers subtly,the adaptively optimal meshes are trend to approximate the transient location precisely,and we apply Matlab programing.As a result,computational costs are saved on the macroscopic scales and the uniformly convergent accuracy is realized for testing norms.