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] and [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.