A Hybrid Mortar Finite Element Method for the Stokes Problem

In this paper, we consider the discretization of the Stokes problem on domain partitions with non-matching meshes. We propose a hybrid mortar method, which is motivated by a variational characterization of solutions of the corresponding interface problem. For the discretization of the subdomain problems, we utilize standard inf-sup stable finite element pairs. The introduction of additional unkowns at the interface allows to reduce the coupling between the subdomain problems, which comes from the variational incorporation of interface conditions. We present a detailed analysis of the hybrid mortar method, in particular, the discrete inf-sup stability condition is proven under weak assumptions on the interface mesh, and optimal a-priori error estimates are derived with respect to the energy and L-norm. For illustration of the results, we present some numerical tests.