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 Stokes- Darcy 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.