Meshfree method for the non-stationary
incompressible Navier-Stokes equations
Hi Jun Choe - Department of Mathematics, Yonsei University, 120-749 SeoDaeMun-gu, Seoul, South Korea (email)
Abstract: 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.
Keywords: Meshfree Method, MLSRK, Stokes Equations, Navier-Stokes Equations, Error Estimate.
Received: November 2004; Revised: July 2005; Published: October 2005.
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