中文摘要：

为处理奇异摄动的对流扩散边界层问题,提出高效的多尺度有限元数值逼近方案.基于先验估计构造特殊的Bakhvalov粗网格,在多尺度格式下利用多尺度基函数有效捕获边界层局部信息.新方法最终在粗网格求解可得到不依赖于小参数e、精度很高的超二阶收敛数值结果,充分体现相比于传统有限元的精度优势.

英文摘要：

A multiscale finite element approximation is proposed to solve the singularly perturbed convection-diffusion boundary layers efficiently.Based on the priori estimate to build Bakhvalov coarse grid,we use the multiscale basis functions to effectively acquire the boundary local information under the multiscale scheme.Through the numerical experiment,our new method on coarse meshes can obtain the highly accurate superconvergence results and independent ε-stability,which shows a great superiority compared to the traditional finite element method.