Meshless method for the stationary incompressible Navier-Stokes equations

Hi Jun Choe; Hyea Hyun Kim; Do Wan Kim; Yongsik Kim

doi:10.3934/dcdsb.2001.1.495

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2001, Volume 1, Issue 4: 495-526. Doi: 10.3934/dcdsb.2001.1.495

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Meshless method for the stationary incompressible Navier-Stokes equations

1.
Department of Mathematics, Yonsei University, 120-749 SeoDaeMun-gu, Seoul
2.
Department of Mathematics, KAIST, 305-701 Taejon
3.
Department of Mathematics, Sunmoon University, 336-708 Asan-si, Chung-Nam

Received: June 30, 2001

Revised: August 31, 2001

Published: October 2001

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Abstract

Mathematical analysis is achieved on a meshless method for the stationary incompressible Stokes and Navier-Stokes equations. In particular, the Moving Least Square Reproducing Kernel (MLSRK) method is employed. The existence of discrete solution and its error estimate are obtained. As a numerical example for convergence analysis, we compute the numerical solutions for these equations to compare with exact solutions. Also we solve the driven cavity flow numerically as a test problem.

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Mathematics Subject Classification: 65D05,65J15,76D05,76M10.

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