January  2006, 6(1): 17-39. doi: 10.3934/dcdsb.2006.6.17

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

1. 

Department of Mathematics, Yonsei University, 120-749 SeoDaeMun-gu, Seoul, South Korea, South Korea

2. 

Department of Mathematics, Sunmoon University, 336-708 Asan-si, Chung-Nam, South Korea

Received  November 2004 Revised  July 2005 Published  October 2005

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.
Citation: Hi Jun Choe, Do Wan Kim, Yongsik Kim. Meshfree method for the non-stationary incompressible Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 17-39. doi: 10.3934/dcdsb.2006.6.17
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