Time accurate consistently stabilized mesh-free methods for convection dominated problems

The behaviour of high-order time stepping methods combined with mesh-free methods is studied for : the transient convection-diffusion equation. Particle methods, such as the element-free Galerkin (EFG) method, allow to easily increase the order of consistency and, thus, to formulate high-order schemes in space and time. Moreover, second derivatives of the EFG shape functions can be constructed with a low extra cost and are well defined, even for linear interpolation. Thus, consistent stabilization schemes can be considered without loss in the convergence rates. Copyright (C) 2003 John Wiley Sons, Ltd.