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

Hi Jun Choe; Do Wan Kim; Yongsik Kim

doi:10.3934/dcdsb.2006.6.17

Article Contents

2006, Volume 6, Issue 1: 17-39. Doi: 10.3934/dcdsb.2006.6.17

This issue Previous Article Homogenization of the Schrödinger equation with a time oscillating potential Next Article Stabilized finite element method for the non-stationary Navier-Stokes problem

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

1.
Department of Mathematics, Yonsei University, 120-749 SeoDaeMun-gu, Seoul
2.
Department of Mathematics, Sunmoon University, 336-708 Asan-si, Chung-Nam

Received: November 2004

Revised: July 2005

Published: January 2006

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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.

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Mathematics Subject Classification: Primary: 65D05, 65J15; Secondary: 76D05, 76M10.

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