November  2001, 1(4): 495-526. doi: 10.3934/dcdsb.2001.1.495

Meshless method for the stationary incompressible Navier-Stokes equations

1. 

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

2. 

Department of Mathematics, KAIST, 305-701 Taejon, South Korea

3. 

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

Received  July 2001 Revised  September 2001 Published  September 2001

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.
Citation: Hi Jun Choe, Hyea Hyun Kim, Do Wan Kim, Yongsik Kim. Meshless method for the stationary incompressible Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2001, 1 (4) : 495-526. doi: 10.3934/dcdsb.2001.1.495
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