摘要
本文讨论了非匹配网格上Stokes-Darcy问题的两种低阶非协调元方法,给出了误差估计,对耦合的非协调元离散问题,通过粗网格求得的界面条件,我们提出了一个解耦的两水平算法.并且我们将两水平方法推广到多水平情形,其只需在一个很粗的网格上解一耦合问题,然后在逐步加细的网格上求解解耦的问题,理论分析和数值试验都说明方法的高效性.
In this paper,two lower order nonconforming finite element methods are presented for the StokesDarcy problem on nonmatching meshes;the optimal error estimates are derived;and a two-level algorithm is also proposed for decoupling the coupled model by a coarse level approximation to the interface coupling conditions.Moreover,we generalize the two-level algorithm to a multilevel algorithm,which solves a coupled problem only on a very coarse mesh and then solves decoupled subproblems on all the subsequently refined meshes.Both theoretical analysis and numerical experiments illustrate the effectiveness and efficiency of these algorithms.
出处
《中国科学：数学》
CSCD
北大核心
2012年第5期389-402,共14页
Scientia Sinica：Mathematica
基金
国家自然科学基金(批准号:11071124和11171154)资助项目
