Journal of the
Korean Mathematical Society JKMS

Mathematical analysis is made on a meshfree method for the compressible Euler equations. In particular, the Moving Least Square Reproducing Kernel (MLSRK) method is employed for space approximation. With the backward-Euler method used for time discretization, existence of discrete solution and it's $L^2$-error estimate are obtained under a regularity assumption of the continuous solution. The result of numerical experiment made on the biconvex airfoil is presented.

Keywords: meshfree method, MLSRK, Euler equations, error estimate

MSC numbers: 65D05, 65J15, 76D05, 76M10