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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

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

Pages: 17 - 39, Volume 6, Issue 1, January 2006

doi:10.3934/dcdsb.2006.6.17       Abstract        Full Text (729.5K)       Related Articles

Hi Jun Choe - Department of Mathematics, Yonsei University, 120-749 SeoDaeMun-gu, Seoul, South Korea (email)
Do Wan Kim - Department of Mathematics, Sunmoon University, 336-708 Asan-si, Chung-Nam, South Korea (email)
Yongsik Kim - 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.
Mathematics Subject Classification:  Primary: 65D05, 65J15; Secondary: 76D05, 76M10.

Received: November 2004;      Revised: July 2005;      Published: October 2005.