Boundary Conditions and Estimates for the Steady Stokes Equations on Staggered Grids

We consider the steady state Stokes equations, describing low speed flow and derive estimates of the solution for various types of boundary conditions. We formulate the boundary conditions in a new way, such that the boundary value problem becomes non-singular. By using a difference approximation on a staggered grid we are able to derive a non-singular approximation in a direct way. Furthermore, we derive the same type of estimates as for the continuous case. Numerical experiments confirm the theoretical results.