非匹配网格上Stokes-Darcy问题非协调元离散的两水平和多水平方法  

Two-level and multilevel methods for Stokes-Darcy problem discretized by nonconforming elements on nonmatching meshes

作　　者：黄佩奇[1] 陈金如[2,3] 

机构地区：[1]南京林业大学应用数学系,南京210037 [2]江苏省大规模复杂系统数值模拟重点实验室,南京210046 [3]南京师范大学数学科学学院,南京210046

出　　处：《中国科学：数学》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

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.

关 键 词：非协调元 非匹配网格 Stokes-Darcy问题 两水平方法 多水平方法 

分 类 号：O241.82[理学—计算数学]