Study on adaptive multiscale finite element method for two-dimensional singularly perturbed problems with two parameters(二维双参数奇异摄动问题的自适应多尺度有限元法探究)

This paper addresses the two-dimensional singularly perturbed partial differentiable equation with two parameters, since the existence of two scaled small parameters it would bring jumps and large errors of the solution. Based on the values of two scaled parameters,we adopt an iterative algorithm to generate a discrete graded mesh, and propose an adaptive multiscale finite element method on the relative coarse mesh to achieve the accurate and efficient solution, therefore reducing errors reasonably. The new method outperforms traditional methods, and shows evident advantages and updated abilities.研究了二维双参数奇异摄动偏微分方程，因2个跨尺度的小参数可能导致其解跳跃，产生较大误差，故基于双参数的实际跨尺度大小，用迭代算法生成离散化分层网格，提出了自适应多尺度有限元法。该方法在粗网格水平上就能精确高效地逼近跳跃解，有效降低误差，其计算优势和改进效果较传统方法有显著的提升。