Discontinuous finite element methods for incompressible flows on subdomains with non-matching interfaces

In this paper, an improved inf–sup condition is derived for a class of discontinuous Galerkin methods for solving the steady-state incompressible Stokes and Navier–Stokes equations. The computational domain is subdivided into subdomains with non-matching meshes at the interfaces. Optimal error estimates are obtained. Numerical experiments including two benchmark problems are presented.