Stokes and Navier-Stokes equations are considered in this paper especially from the numerical point of view. Numerical analysis of a discontinuous Galerkin method with nonoverlapping domain decomposition for steady incompressible Stokes and Navier-Stokes problems is investigated. As a discretization a conforming triangular finite element mesh is used in each subdomain. In each triangle the discretization velocity is a polynomial of degree

$k,$ $\phantom{\rule{4pt}{0ex}}k=1,\phantom{\rule{4pt}{0ex}}2\phantom{\rule{4.pt}{0ex}}\text{or}\phantom{\rule{4.pt}{0ex}}3$, while the discretized pressure is of degree

$k-1$. The variational formulation of the problem contains also a jump term on all triangle interfaces due to the domain decomposition method. An inf-sup condition is proved under some hypothesis for the domain decomposition with non-matching grids. Optimal a priori error estimates in the energy norm for the velocity field and the

${L}_{2}$ norm for the pressure are derived first for Stokes and then also for Navier-Stokes problems.