Mortar formulation for a class of staggered discontinuous Galerkin methods

A mortar formulation is developed and analyzed for a class of staggered discontinuous Galerkin (SDG) methods applied to second order elliptic problems in two dimensions. The computational domain consists of nonoverlapping subdomains and a triangulation is provided for each subdomain, which need not conform across subdomain interfaces. This feature allows a more flexible design of discrete models for problems with complicated geometries, shocks, or singular points. A mortar matching condition is enforced on the solutions across the subdomain interfaces by introducing a Lagrange multiplier space. Moreover, optimal convergence rates in both L2L2 and discrete energy norms are proved. Numerical results are presented to show the performance of the method.