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In this paper, we propose a new virtual interpolation point method toformulate the discrete Stokes equations. We form virtual staggered structurefor the velocity and pressure from the actual computation node set. The virtualinterpolation point method by a point collocation scheme is well suited tomeshfree scheme since the approximation comes from smooth kernel and we candifferentiate directly the kernels. The focus of this paper is laid on thecontribution to a stable flow computation without explicit structure ofstaggered grid. In our method, we don't have to construct explicitly thestaggered grid at all. Instead, there exists only virtual interpolation pointsat each computational node which play a key role in discretizing theconservative quantities of the Stokes equations.  We prove the inf-sup condition for virtual interpolation point method withvirtual structure of staggered grid and the existence and stability of discretesolutions.

Existence and stability in a virtual interpolation method of the Stokes equations