Existence and stability in the virtual interpolation point method for the Stokes equations

In this paper, we propose a novel virtual interpolation point (VIP) method formulating discrete Stokes equations. We have formed virtual staggered structure for velocity and pressure from the actual computation node set. The VIP method by a point collocation scheme is well suited for meshfree scheme because the approximation comes from smooth kernels and kernels can be differentiated directly. This paper highlights our contribution to a stable flow computation without explicit structure of staggered grid. Our method eliminates the need to construct explicit staggered grid. Instead, virtual interpolation nodes play key roles in discretizing the conservative quantities of the Stokes equations. We have proved the inf-sup condition for VIP method with virtual structure of staggered grid and thus the existence and stability of discrete solutions follow.