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

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.

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

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.