A class of hybrid mortar finite element methods for interface problems with non-matching meshes

In this paper, we propose and analyze a family of hybrid finite element methods for interface problems with possibly non-matching meshes. These methods are related to hybrid mixed finite element methods and discontinuous Galerkin methods, as well as Nitsche-type mortaring techniques, but overcome some of the disadvantages of these. By introducing the additional hybrid variable, we obtain methods that allow for subassembling on the subdomain level yielding positive definite global systems. Moreover, the primal unknowns can be eliminated by solving local Dirichlet problems on the subdomains, yielding Schur complement systems for the hybrid variables only. In contrast to dual domain decomposition and mortar methods, the space for the hybrid variable can be chosen with great flexibility without perturbing the stability. We derive the basic a-priori error estimates in energy and L-norm, and confirm the theoretical results by numerical tests.