Meshfree method for the non-stationary incompressible Navier-Stokes equations

We consider the solvability and the error estimates of numerical solutions of the non-stationary incompressible Stokes and Navier-Stokes equations by the meshfree method. The moving least square reproducing kernel method or the MLSRK method is employed for the space approximations. The existence of numerical solutions and the $L^2$-type error estimates are obtained. As a numerical example, we compare the numerical solutions of the Stokes and the Navier-Stokes equations with the exact solutions. Also we solve the non-stationary Navier-Stokes driven cavity flow using the MLSRK method.