DCDS-B
Meshless method for the stationary incompressible Navier-Stokes equations
Hi Jun Choe Hyea Hyun Kim Do Wan Kim Yongsik Kim
Discrete & Continuous Dynamical Systems - B 2001, 1(4): 495-526 doi: 10.3934/dcdsb.2001.1.495
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.
keywords: Meshless method Stokes equations Navier-Stokes equations MLSRK error estimate.
DCDS-B
Meshfree method for the non-stationary incompressible Navier-Stokes equations
Hi Jun Choe Do Wan Kim Yongsik Kim
Discrete & Continuous Dynamical Systems - B 2006, 6(1): 17-39 doi: 10.3934/dcdsb.2006.6.17
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: MLSRK Stokes Equations Meshfree Method Navier-Stokes Equations Error Estimate.

Year of publication

Related Authors

Related Keywords

[Back to Top]