An enriched discontinuous Galerkin formulation for the coupling of non-conforming meshes

Finite element modeling using non-conforming meshes requires an interface model that ensures geometric compatibility and a complete transfer of surface tractions between the connecting elements at the non-conforming interfaces. Most currently available coupling methods are dual approaches that employ a field of Lagrange multipliers to enforce geometric compatibility at the interface. The choice of the Lagrange multiplier field is not trivial since not all possible interpolations satisfy the inf-sup or Ladyzhenskaya-Babuška-Brezzi (LBB) condition. The primal discontinuous Galerkin (DG) and Nitsche methods are not subject to the LBB restrictions, however, in both these methods a mesh-dependent penalty parameter is required to ensure stability [24,2]. We propose a primal interface formulation that makes use of a local enrichment of the interface elements to enable an unbiased enforcement of geometric compatibility at all interface nodes without inducing over-constraint and without introducing additional variables. We show that a local DG-based interface stabilization procedure guarantees a consistent transfer of the traction field across the non-conforming interface.